Wikipedia:WikiProject Mathematics/PlanetMath Exchange/54-XX General topology

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This page provides a list of all articles available at PlanetMath in the following topic:

54-XX General topology.

This list will be periodically updated. Each entry in the list has three fields:

1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:

Status	means PM article
N	not needed
A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

• Please update the WP and Status fields as appropriate.
• if the WP field is correct please remove the qualifier "guess".
• If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
• If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
• If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

• {{planetmath|id=|title=}} for copied over text
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See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

[edit] 54-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: bibliography for topology, id=6260 -- WP: List of publications in mathematics#Topology -- Status: NC

Do we want to start creating Bibliograhies? Paul August ☎ 20:15, Feb 1, 2005 (UTC)

• PM: boundary / frontier, id=4200 -- WP: boundary (topology), manifold -- Status: A

Paul August ☎ 20:15, Feb 1, 2005 (UTC)

• PM: characterizations of connectedness, id=6249 -- WP: Connected space -- Status: A

The PM article does have a proof of some equivalent conditions to connected, but I don't really think we need it. Paul August ☎ 04:35, Feb 2, 2005 (UTC)

• PM: closed set, id=2739 -- WP: closed set -- Status: NM

Paul August ☎ 04:08, Mar 14, 2005 (UTC)

• PM: coarser, id=3290 -- WP: Comparison of topologies -- Status: A

• PM: compact-open topology, id=3976 -- WP: compact-open topology -- Status: A

Paul August ☎ 04:53, Feb 2, 2005 (UTC)

• PM: completely normal, id=1606 -- WP: completely normal -- Status: A

Completely normal redirects to normal space, but I think it could have its own article. Paul August ☎ 03:21, 1 September 2006 (UTC)

• PM: continuous proper map, id=4190 -- WP: proper map -- Status: A

• PM: derived set, id=4207 -- WP: derived set -- Status: A

AdamSmithee 14:31, 16 January 2006 (UTC)

• PM: diameter, id=1989 -- WP: diameter -- Status: NM

AdamSmithee 14:31, 16 January 2006 (UTC)

• PM: every second countable space is separable, id=2119 -- WP: second countable space -- Status: A

Paul August ☎ 20:21, 3 September 2006 (UTC)

• PM: first axiom of countability, id=2120 -- WP: first-countable space -- Status: A

Paul August ☎ 03:27, 1 September 2006 (UTC)

• PM: homotopy groups, id=1641 -- WP: homotopy groups -- Status: NM

Paul August ☎ 17:28, 17 October 2006 (UTC)

• PM: index of properties of topolological spaces, id=6251 -- WP: topological property -- Status: NM

Paul August ☎ 18:38, 23 October 2006 (UTC)

• PM: indiscrete topology, id=3120 -- WP: trivial topology -- Status: A

Paul August ☎ 04:11, 1 September 2006 (UTC)

• PM: interior, id=3123 -- WP: interior -- Status: NM

The interior operator stuff uses a nicer notation in PM AdamSmithee 14:31, 16 January 2006 (UTC)

Change to NM, the nicer PM layout should be merged in. linas 16:36, 26 November 2006 (UTC)

• PM: invariant forms on representations of compact groups, id=3933 -- WP guess: invariant forms on representations of compact groups -- Status:

• PM: Krull dimension, id=1107 -- WP guess: Krull dimension -- Status:

• PM: ladder connected, id=4867 -- WP guess: ladder connected -- Status:

• PM: local base, id=2121 -- WP: local base -- Status: A

Paul August ☎ 19:22, 1 September 2006 (UTC)

• PM: loop, id=1706 -- WP: loop (topology) -- Status: A

Loop (topology) redirects to Path (topology), but it could have it's own article. Paul August ☎ 19:52, 1 September 2006 (UTC)

• PM: loop space, id=1640 -- WP guess: loop space -- Status:

• PM: metacompact, id=8170 -- WP: metacompact space -- Status: A

Paul August ☎ 01:45, 23 October 2006 (UTC)

• PM: neighborhood system, id=2124 -- WP: neighbourhood system -- Status: A

AdamSmithee 14:31, 16 January 2006 (UTC)

• PM: Niemytzki plane, id=4247 -- WP: Niemytzki plane -- Status: NC

Paul August ☎ 04:22, 3 September 2006 (UTC)

• PM: paracompact topological space, id=1540 -- WP: paracompact space -- Status: A

Paul August ☎ 20:13, 1 September 2006 (UTC)

• PM: Peano space, id=8001 -- WP: Peano space -- Status: A

Paul August ☎ 02:38, 23 October 2006 (UTC)

• PM: pointed topological space, id=4965 -- WP: pointed topological space -- Status: A

Paul August ☎ 03:57, 3 September 2006 (UTC)

• PM: proper map, id=4801 -- WP: proper map -- Status: A.

Oleg Alexandrov (talk) 02:05, 24 July 2006 (UTC)

• PM: quasi-compact, id=1642 -- WP: quasi-compact -- Status: A

Paul August ☎ 03:54, 3 September 2006 (UTC)

• PM: regularly open, id=1954 -- WP: regular open set -- Status: A

Regular open set redirects to topological glossary, but could have its own article.

• PM: support of function, id=4475 -- WP: support of function -- Status: NM

Properties, particularly 5 and 6 AdamSmithee 14:31, 16 January 2006 (UTC)

• PM: topological invariant, id=4378 -- WP: topological invariant -- Status: A

AdamSmithee 14:31, 16 January 2006 (UTC)

• PM: triangle inequality, id=1629 -- WP: triangle inequality -- Status: A

AdamSmithee 14:31, 16 January 2006 (UTC)

• PM: universal covering space, id=1643 -- WP guess: universal covering space -- Status:

• PM: zero dimensional, id=6291 -- WP: zero dimensional space -- Status: A

Paul August ☎ 20:30, 3 September 2006 (UTC)

• PM: discrete space, id=2726^new! -- WP: discrete space -- Status: NM

Paul August ☎ 02:52, 23 October 2006 (UTC)

• PM: finite and countable discrete spaces, id=7077^new! -- WP: discrete space -- Status: A

Paul August ☎ 20:03, 23 October 2006 (UTC)

• PM: locally homeomorphic, id=7020^new! -- WP: Local homeomorphism -- Status: NM

Paul August ☎ 20:17, 23 October 2006 (UTC)

• PM: separated, id=7064^new! -- WP: separated sets -- Status: A

• PM: when are balls separated, id=7066^new! -- WP: (none) -- Status: N

Paul August ☎ 03:38, 6 September 2006 (UTC)

[edit] 54A05 Topological spaces and generalizations (closure spaces, etc.)

• PM: F_\sigma set, id=6215 -- WP: F-sigma set -- Status: A

Paul August ☎ 03:04, 9 September 2006 (UTC)

• PM: G_\delta set, id=6216 -- WP: G-delta set -- Status: A

Paul August ☎ 03:04, 9 September 2006 (UTC)

• PM: characterization of connected compact metric spaces., id=5473 -- WP guess: characterization of connected compact metric spaces. -- Status:

• PM: classification of topological properties according to behaviour under mapping, id=6217 -- WP guess: classification of topological properties according to behaviour under mapping -- Status:

• PM: closure axioms, id=3697 -- WP guess: closure axioms -- Status:

• PM: countable complement topology, id=6214 -- WP guess: countable complement topology -- Status:

• PM: finite complement topology, id=6213 -- WP: finite complement topology -- Status: M

Paul August ☎ 23:19, 28 October 2006 (UTC)

• PM: isolated, id=1201 -- WP: isolated point -- Status: A

AdamSmithee 14:51, 16 January 2006 (UTC)

• PM: Jordan curve theorem, id=3587 -- WP: Jordan curve theorem -- Status: A

Paul August ☎ 05:00, 24 October 2006 (UTC)

• PM: limit points of sequences, id=6220 -- WP guess: limit points of sequences -- Status:

• PM: neighborhood, id=1151 -- WP: neighbourhood (mathematics) -- Status: A

AdamSmithee 14:51, 16 January 2006 (UTC)

• PM: open set, id=2925 -- WP guess: open set -- Status:

• PM: proof of characterization of connected compact metric spaces., id=5739 -- WP guess: proof of characterization of connected compact metric spaces. -- Status:

• PM: coercive function, id=7154^new! -- WP guess: coercive function -- Status:

• PM: composition with coercive function, id=7155^new! -- WP guess: composition with coercive function -- Status:

[edit] 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

• PM: alternative characterization of ultrafilter, id=6324 -- WP guess: alternative characterization of ultrafilter -- Status:

• PM: another proof of Dini's theorem, id=5437 -- WP guess: another proof of Dini's theorem -- Status:

• PM: Banach fixed point theorem, id=2758 -- WP: Banach fixed point theorem -- Status: A

Paul August ☎ 05:06, 24 October 2006 (UTC)

• PM: continuous convergence, id=5445 -- WP guess: continuous convergence -- Status:

• PM: contractive maps are uniformly continuous, id=4481 -- WP guess: contractive maps are uniformly continuous -- Status:

• PM: Dini's theorem, id=1988 -- WP guess: Dini's theorem -- Status:

• PM: every filter is contained in an ultrafilter, id=6304 -- WP guess: every filter is contained in an ultrafilter -- Status:

• PM: net, id=3250 -- WP: net (mathematics) -- Status: A

linas 00:06, 22 November 2006 (UTC)

• PM: proof of alternative characterization of ultrafilter, id=6325 -- WP guess: proof of alternative characterization of ultrafilter -- Status:

• PM: proof of Banach fixed point theorem, id=3581 -- WP guess: proof of Banach fixed point theorem -- Status:

• PM: proof of Dini's theorem, id=3038 -- WP guess: proof of Dini's theorem -- Status:

• PM: proof that every filter is contained in an ultrafilter, id=6305 -- WP guess: proof that every filter is contained in an ultrafilter -- Status:

• PM: theorem about continuous convergence, id=5446 -- WP guess: theorem about continuous convergence -- Status:

• PM: ultrafilter, id=1611 -- WP guess: ultrafilter -- Status:

• PM: ultranet, id=3260 -- WP: ultranet (math) -- Status: A

linas 00:09, 22 November 2006 (UTC)

[edit] 54A99 Miscellaneous

• PM: U\cap \overline{E} \subseteq \overline{U\cap E} when U is open and E is any set, id=6266 -- WP guess: U\cap \overlineE \subseteq \overlineU\cap E when U is open and E is any set -- Status:

• PM: absolute retract, id=6253 -- WP guess: absolute retract -- Status:

• PM: adherent point, id=6224 -- WP: adherent point -- Status: C

linas 04:08, 27 November 2006 (UTC)

• PM: basis (topology), id=1161 -- WP: basis (topology) -- Status: A

linas 21:49, 24 November 2006 (UTC)

• PM: box topology, id=3095 -- WP: box topology -- Status: A

linas 00:36, 22 November 2006 (UTC)

• PM: closure, id=1191 -- WP: Closure (topology) -- Status: A

AdamSmithee 15:11, 16 January 2006 (UTC)

• PM: conditions for a collection of subsets to be a basis for some topology, id=5845 -- WP guess: conditions for a collection of subsets to be a basis for some topology -- Status:

• PM: cover, id=1224 -- WP guess: cover -- Status:

• PM: dense, id=1192 -- WP: Dense set -- Status: A

AdamSmithee 15:11, 16 January 2006 (UTC)

• PM: dense in-itself, id=6228 -- WP: dense-in-itself -- Status: C

Physicistjedi 05:06, December 8 2006 (UTC)

• PM: identification topology, id=6299 -- WP guess: identification topology -- Status:

• PM: limit point, id=1240 -- WP: limit point -- Status: NM

I especially like the wording where PM explains the meaning of limit in the name limit point AdamSmithee 15:11, 16 January 2006 (UTC)

• PM: neighborhood retract, id=6255 -- WP: neighborhood retract -- Status: M

linas 23:48, 24 November 2006 (UTC)

• PM: nowhere dense, id=3025 -- WP: nowhere dense -- Status: A

AdamSmithee 15:11, 16 January 2006 (UTC)

• PM: perfect set, id=3821 -- WP guess: perfect set -- Status:

• PM: proof of properties of the closure operator, id=5638 -- WP guess: proof of properties of the closure operator -- Status:

• PM: properties of the closure operator, id=4474 -- WP guess: properties of the closure operator -- Status:

• PM: shrinking of cover, id=6258 -- WP guess: shrinking of cover -- Status:

• PM: subbasis, id=1409 -- WP: subbasis -- Status: A

linas 21:54, 24 November 2006 (UTC)

• PM: topological sum, id=6300 -- WP guess: topological sum -- Status:

• PM: types of limit points, id=6211 -- WP: limit point -- Status: NM

AdamSmithee 15:11, 16 January 2006 (UTC)

• PM: a nonempty perfect subset of \mathbb{R} that contains no rational number, id=7283^new! -- WP guess: a nonempty perfect subset of \mathbbR that contains no rational number -- Status:

• PM: properties of the closure operator, id=7075^new! -- WP guess: properties of the closure operator -- Status:

[edit] 54B05 Subspaces

• PM: subspace topology, id=499 -- WP guess: subspace topology -- Status:

• PM: characterization of subspace topology, id=7616^new! -- WP guess: characterization of subspace topology -- Status:

• PM: closed set in a subspace, id=7460^new! -- WP guess: closed set in a subspace -- Status:

• PM: subspace of a subspace, id=7096^new! -- WP guess: subspace of a subspace -- Status:

• PM: subspace topology in a metric space, id=7093^new! -- WP guess: subspace topology in a metric space -- Status:

[edit] 54B10 Product spaces

• PM: product topology, id=3100 -- WP: product topology -- Status: A

linas 00:28, 22 November 2006 (UTC)

• PM: product topology preserves the Hausdorff property, id=4317 -- WP: product topology preserves the Hausdorff property -- Status: N

Article is a proof, added a link to it in product topology. linas 00:40, 22 November 2006 (UTC)

• PM: product topology and subspace topology, id=7504 -- WP: product topology and subspace topology -- Status: N

Article is a proof, added a link to it in initial topology. linas 01:14, 26 November 2006 (UTC)

[edit] 54B15 Quotient spaces, decompositions

• PM: cell attachment, id=3991 -- WP guess: cell attachment -- Status:

• PM: Klein bottle, id=4249 -- WP: Klein bottle -- Status:

• PM: Möbius strip, id=3278 -- WP: Möbius strip -- Status:

• PM: quotient space, id=2930 -- WP: quotient space -- Status: A

linas 20:38, 25 November 2006 (UTC)

[edit] 54B17 Adjunction spaces and similar constructions

• PM: adjunction space, id=3992 -- WP: adjunction space -- Status: A

linas 01:34, 26 November 2006 (UTC)

[edit] 54B40 Presheaves and sheaves

• PM: direct image, id=1100 -- WP guess: direct image -- Status:

[edit] 54B99 Miscellaneous

• PM: cofinite and cocountable topology, id=3464 -- WP: cofinite and cocountable topology -- Status: A

linas 19:03, 24 November 2006 (UTC)

• PM: cone, id=3974 -- WP: cone (topology) -- Status: M

WP article is missing definition of a reduced cone on pointed spaces.linas 21:49, 25 November 2006 (UTC)

Now Merged. linas 02:10, 26 November 2006 (UTC)

• PM: join, id=3985 -- WP: join (topology) -- Status: M

linas 22:00, 25 November 2006 (UTC)

• PM: order topology, id=1411 -- WP: order topology -- Status: M

Previously merged by User:Lethe in Dec 2005.

• PM: suspension, id=3984 -- WP: suspension (topology) -- Status: M

linas 02:02, 26 November 2006 (UTC)

• PM: initial topology, id=7368 -- WP: initial topology -- Status: A

linas 17:02, 25 November 2006 (UTC)

[edit] 54C05 Continuous maps

• PM: homeomorphism, id=912 -- WP guess: homeomorphism -- Status:

• PM: Inverse Function Theorem (topological spaces), id=3965 -- WP guess: Inverse Function Theorem (topological spaces) -- Status:

• PM: proof of Inverse Function Theorem (topological spaces), id=4125 -- WP guess: proof of Inverse Function Theorem (topological spaces) -- Status:

• PM: continuity is preserved when codomain is extended, id=7078^new! -- WP guess: continuity is preserved when codomain is extended -- Status:

• PM: gluing together continuous functions, id=7081^new! -- WP guess: gluing together continuous functions -- Status:

[edit] 54C10 Special maps on topological spaces (open, closed, perfect, etc.)

• PM: open mapping, id=3676 -- WP guess: open mapping -- Status:

[edit] 54C15 Retraction

• PM: retract, id=1693 -- WP: retract -- Status: A

linas 23:36, 24 November 2006 (UTC)

[edit] 54C20 Extension of maps

• PM: proof of Tietze extension theorem, id=5566 -- WP: Tietze extension theorem -- Status: N

Added as link in article. linas 23:39, 24 November 2006 (UTC)

[edit] 54C25 Embedding

[edit] 54C30 Real-valued functions

[edit] 54C40 Algebraic properties of function spaces

[edit] 54C70 Entropy

• PM: differential entropy, id=1915 -- WP guess: differential entropy -- Status:

[edit] 54C99 Miscellaneous

• PM: Borsuk-Ulam theorem, id=947 -- WP guess: Borsuk-Ulam theorem -- Status:

• PM: ham sandwich theorem, id=4772 -- WP guess: ham sandwich theorem -- Status:

• PM: proof of Borsuk-Ulam theorem, id=3621 -- WP guess: proof of Borsuk-Ulam theorem -- Status:

[edit] 54D05 Connected and locally connected spaces (general aspects)

• PM: clopen subset, id=3978 -- WP guess: clopen subset -- Status:

• PM: connected component, id=948 -- WP guess: connected component -- Status:

• PM: connected set, id=4482 -- WP guess: connected set -- Status:

• PM: connected set in a topological space, id=4811 -- WP guess: connected set in a topological space -- Status:

• PM: connected space, id=941 -- WP guess: connected space -- Status:

• PM: connectedness is preserved under a continuous map, id=4692 -- WP guess: connectedness is preserved under a continuous map -- Status:

• PM: cut-point, id=4706 -- WP guess: cut-point -- Status:

• PM: example of a connected space that is not path-connected, id=3087 -- WP guess: example of a connected space that is not path-connected -- Status:

• PM: example of a semilocally simply connected space which is not locally simply connected, id=3972 -- WP guess: example of a semilocally simply connected space which is not locally simply connected -- Status:

• PM: example of a space that is not semilocally simply connected, id=3967 -- WP guess: example of a space that is not semilocally simply connected -- Status:

• PM: hyperconnected space, id=5813 -- WP: hyperconnected space -- Status: A

linas 17:17, 24 November 2006 (UTC)

• PM: locally connected, id=2912 -- WP guess: locally connected -- Status:

• PM: locally simply connected, id=3975 -- WP guess: locally simply connected -- Status:

• PM: path, id=942 -- WP guess: path -- Status:

• PM: path component, id=949 -- WP guess: path component -- Status:

• PM: products of connected spaces are connected, id=4697 -- WP guess: products of connected spaces are connected -- Status:

• PM: proof that a path connected space is connected, id=3086 -- WP guess: proof that a path connected space is connected -- Status:

• PM: proof that products of connected spaces are connected, id=5592 -- WP guess: proof that products of connected spaces are connected -- Status:

• PM: quasicomponent, id=2201 -- WP guess: quasicomponent -- Status:

• PM: semilocally simply connected, id=2911 -- WP guess: semilocally simply connected -- Status:

• PM: ultraconnected space, id=5814 -- WP: ultraconnected space -- Status: C

linas 17:27, 24 November 2006 (UTC)

• PM: limit points and closure for connected sets, id=7097^new! -- WP guess: limit points and closure for connected sets -- Status:

• PM: union of non-disjoint connected sets is connected, id=7095^new! -- WP guess: union of non-disjoint connected sets is connected -- Status:

[edit] 54D10 Lower separation axioms (T0--T3, etc.)

• PM: a compact set in a Hausdorff space is closed, id=4194 -- WP guess: a compact set in a Hausdorff space is closed -- Status:

• PM: a space \mathnormal{X} is Hausdorff if and only if \Delta(X) is closed, id=5820 -- WP guess: a space \mathnormalX is Hausdorff if and only if \Delta(X) is closed -- Status:

• PM: a space is T1 if and only if every singleton is closed, id=5808 -- WP guess: a space is T1 if and only if every singleton is closed -- Status:

• PM: a space is T1 if and only if every subset A is the intersection of all open sets containing A, id=5809 -- WP guess: a space is T1 if and only if every subset A is the intersection of all open sets containing A -- Status:

• PM: characterization of T2 spaces, id=6306 -- WP guess: characterization of T2 spaces -- Status:

• PM: completely Hausdorff, id=5717 -- WP: completely Hausdorff -- Status: A

linas 19:35, 24 November 2006 (UTC)

• PM: functionally Hausdorff \Rightarrow completely Hausdorff \Rightarrow Hausdorff, id=6323 -- WP guess: functionally Hausdorff \Rightarrow completely Hausdorff \Rightarrow Hausdorff -- Status:

• PM: Hausdorff space not completely Hausdorff, id=5718 -- WP: Hausdorff space not completely Hausdorff -- Status: NC

Nice counterexample. linas 19:44, 24 November 2006 (UTC)

• PM: metric spaces are Hausdorff, id=5838 -- WP: metric space -- Status: N

This is a proof of a theorem, and was linked as such in metric space. linas 18:44, 22 November 2006 (UTC)

• PM: point and a compact set in a Hausdorff space have disjoint open neighborhoods., id=4193 -- WP: Hausdorff space -- Status: N

A proof, added as link to Hausdorff space. linas 02:32, 26 November 2006 (UTC)

• PM: proof of A compact set in a Hausdorff space is closed, id=4203 -- WP: Hausdorff space -- Status: N

This is a proof, added link to article on Hausdorff space. linas 02:26, 26 November 2006 (UTC)

• PM: regular space, id=1863 -- WP: regular space -- Status: A

linas 20:18, 24 November 2006 (UTC)

• PM: separation axioms, id=4050 -- WP: separation axioms -- Status: A

linas 02:35, 26 November 2006 (UTC)

• PM: T0 space, id=1850 -- WP: T0 space -- Status: A

linas 19:53, 24 November 2006 (UTC)

• PM: T1 space, id=1852 -- WP: T1 space -- Status: A

linas 20:01, 24 November 2006 (UTC)

• PM: T2 space, id=1855 -- WP guess: T2 space -- Status: A

linas 20:05, 24 November 2006 (UTC)

• PM: T3 space, id=1866 -- WP: T3 space -- Status: A

linas 20:07, 24 November 2006 (UTC)

• PM: topological space is T_1 if and only if every singleton is closed., id=4183 -- WP guess: topological space is T_1 if and only if every singleton is closed. -- Status:

• PM: two disjoint compact sets in a Hausdorff space have disjoint open neighborhoods., id=4195 -- WP: Hausdorff space -- Status:

PM link is currently borken. linas 02:42, 26 November 2006 (UTC)

• PM: a space is T_1 if and only if distinct points are separated, id=7069^new! -- WP guess: a space is T_1 if and only if distinct points are separated -- Status:

• PM: Hausdorff property is hereditary, id=7202 -- WP: Hausdorff space -- Status: N

Its a proof, added as a link to Hausdorff space. linas 02:39, 26 November 2006 (UTC)

[edit] 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• PM: T4 space, id=6318 -- WP: T4 space -- Status: A

linas 20:26, 24 November 2006 (UTC)

• PM: normal, id=1532 -- WP: normal space -- Status: A

linas 20:27, 24 November 2006 (UTC)

• PM: proof of Urysohn's lemma, id=3597 -- WP: proof of Urysohn's lemma -- Status: N

Added as link from Urysohn's lemma. linas 20:52, 24 November 2006 (UTC)

• PM: Tietze extension theorem, id=4215 -- WP: Tietze extension theorem -- Status: A

linas 20:58, 24 November 2006 (UTC)

• PM: Tychonoff, id=1534 -- WP: Tychonoff space -- Status: A

linas 21:19, 24 November 2006 (UTC)

• PM: Urysohn's lemma, id=1530 -- WP: Urysohn's lemma -- Status: A

linas 20:41, 24 November 2006 (UTC)

[edit] 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)

• PM: collectionwise normal, id=6497 -- WP guess: collectionwise normal -- Status:

• PM: countably compact, id=1233 -- WP guess: countably compact -- Status:

• PM: development, id=6495 -- WP: development (topology) -- Status: C

linas 17:25, 19 November 2006 (UTC)

• PM: Lindelöf, id=1226 -- WP guess: Lindelöf -- Status:

• PM: locally finite, id=1542 -- WP: locally finite -- Status: A

PM is dictdef, WP is link to glossary. linas 22:35, 24 November 2006 (UTC)

• PM: partition of unity, id=4063 -- WP guess: partition of unity -- Status:

• PM: point finite collection, id=6256 -- WP guess: point finite collection -- Status:

[edit] 54D30 Compactness

• PM: Y is compact if and only if every open cover of Y has a finite subcover, id=4179 -- WP guess: Y is compact if and only if every open cover of Y has a finite subcover -- Status:

• PM: a space is compact if and only if the space has the finite intersection property, id=4181 -- WP guess: a space is compact if and only if the space has the finite intersection property -- Status:

• PM: closed set in a compact space is compact, id=4177 -- WP guess: closed set in a compact space is compact -- Status:

• PM: closed subsets of a compact set are compact, id=4691 -- WP guess: closed subsets of a compact set are compact -- Status:

• PM: compact, id=503 -- WP guess: compact -- Status:

• PM: compactness is preserved under a continuous map, id=4689 -- WP guess: compactness is preserved under a continuous map -- Status:

• PM: examples of compact spaces, id=3133 -- WP guess: examples of compact spaces -- Status:

• PM: finite intersection property, id=4178 -- WP guess: finite intersection property -- Status:

• PM: Heine-Borel theorem, id=1165 -- WP: Heine-Borel theorem -- Status: A

AdamSmithee 15:18, 16 January 2006 (UTC)

• PM: limit point compact, id=1234 -- WP guess: limit point compact -- Status:

• PM: proof of Heine-Borel theorem, id=3328 -- WP: Heine-Borel theorem -- Status: N

AdamSmithee 15:18, 16 January 2006 (UTC)

• PM: properties of compact spaces, id=3966 -- WP guess: properties of compact spaces -- Status:

• PM: pseudocompact space, id=5815 -- WP guess: pseudocompact space -- Status:

• PM: relatively compact, id=4722 -- WP guess: relatively compact -- Status:

• PM: representation theorem for compact metric spaces, id=6265 -- WP guess: representation theorem for compact metric spaces -- Status:

• PM: Stone-\v Cech compactification, id=6207 -- WP guess: Stone-Cech compactification -- Status:

• PM: Tychonoff's theorem, id=1168 -- WP: Tychonoff's theorem -- Status: A

linas 21:22, 24 November 2006 (UTC)

• PM: weakly countably compact, id=6212 -- WP guess: weakly countably compact -- Status:

• PM: proof of Tychonoff's theorem in finite case, id=7288 -- WP: proof of Tychonoff's theorem in finite case -- Status: N

Linked proof to Tychonoff's theorem linas 21:29, 24 November 2006 (UTC)

[edit] 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)

• PM: Alexandrov one-point compactification, id=4515 -- WP guess: compactification (mathematics) -- Status:

• PM: compactification, id=1654 -- WP guess: compactification (mathematics) -- Status:

[edit] 54D45 Local compactness, $\sigma$-compactness

• PM: \sigma-compact, id=5503 -- WP guess: Sigma-compactness -- Status:

• PM: examples of locally compact and not locally compact spaces, id=3129 -- WP guess: examples of locally compact and not locally compact spaces -- Status:

• PM: locally compact, id=2904 -- WP guess: locally compact -- Status:

• PM: precompact set, id=6264 -- WP guess: precompact set -- Status:

[edit] 54D65 Separability

• PM: separable, id=1193 -- WP: separable space -- Status: A

linas 18:35, 22 November 2006 (UTC)

[edit] 54D70 Base properties

• PM: second countable, id=1162 -- WP: second countable -- Status: A

linas 22:07, 24 November 2006 (UTC)

• PM: second countability is hereditary, id=7208 -- WP: second-countable space -- Status: A

linas 22:09, 24 November 2006 (UTC)

[edit] 54D99 Miscellaneous

• PM: first countable, id=2187 -- WP: first countable -- Status: A

linas 18:33, 22 November 2006 (UTC)

• PM: Lindelöf theorem, id=2118 -- WP guess: Lindelof theorem -- Status:

• PM: proof of Lindelöf theorem, id=3299 -- WP guess: Lindelof theorem -- Status:

• PM: totally disconnected space, id=3981 -- WP guess: totally disconnected space -- Status:

[edit] 54E05 Proximity structures and generalizations

• PM: Moore space, id=6496 -- WP: Moore space (topology) -- Status: C

linas 16:12, 19 November 2006 (UTC)

[edit] 54E15 Uniform structures and generalizations

• PM: topology induced by uniform structure, id=3091 -- WP guess: topology induced by uniform structure -- Status:

• PM: uniform space, id=3085 -- WP guess: uniform space -- Status:

• PM: uniform structure of a metric space, id=3103 -- WP guess: uniform structure of a metric space -- Status:

• PM: uniform structure of a topological group, id=3104 -- WP guess: uniform structure of a topological group -- Status:

[edit] 54E25 Semimetric spaces

• PM: hemimetric, id=5903 -- WP: hemimetric -- Status: C

linas 06:37, 22 November 2006 (UTC)

• PM: semimetric, id=5904 -- WP: semimetric -- Status: N

PM article is blanked, because it gave the wrong definition (it confused quasimetric with semi-metric). linas 06:19, 22 November 2006 (UTC)

[edit] 54E30 Moore spaces

• PM: relatively prime integer topology, id=6314 -- WP guess: relatively prime integer topology -- Status:

[edit] 54E35 Metric spaces, metrizability

• PM: \varepsilon-net, id=4280^new! -- WP guess: \varepsilon-net -- Status:

• PM: alternative definition of metric space, id=6903^new! -- WP guess: alternative definition of metric space -- Status:

• PM: ball, id=1296^new! -- WP guess: ball -- Status:

• PM: bounded, id=4826^new! -- WP guess: bounded -- Status:

• PM: bounded, id=1167^new! -- WP guess: bounded -- Status:

• PM: city-block metric, id=1552^new! -- WP guess: city-block metric -- Status:

• PM: completely metrizable, id=1609^new! -- WP guess: completely metrizable -- Status:

• PM: distance to a set, id=4294^new! -- WP guess: distance to a set -- Status:

• PM: equibounded, id=3766^new! -- WP guess: equibounded -- Status:

• PM: example of pseudometric space, id=6275 -- WP: pseudometric space -- Status: M

linas 18:24, 22 November 2006 (UTC)

• PM: examples of metric spaces, id=6833^new! -- WP guess: examples of metric spaces -- Status:

• PM: Hausdorff metric, id=4046 -- WP: Hausdorff metric -- Status: NM

linas 17:07, 24 November 2006 (UTC)

• PM: Hausdorff metric inherits completeness, id=5563^new! -- WP guess: Hausdorff metric inherits completeness -- Status:

• PM: isometry, id=1931^new! -- WP guess: isometry -- Status:

• PM: metric space, id=498 -- WP: metric space -- Status: A

linas 18:27, 22 November 2006 (UTC)

• PM: open set in \mathbb{R}^n contains an open rectangle, id=5537^new! -- WP guess: open set in \mathbbR^n contains an open rectangle -- Status:

• PM: point countable base, id=6499^new! -- WP guess: point countable base -- Status:

• PM: pseudometric space, id=6273 -- WP: pseudometric space -- Status: C

linas 16:20, 22 November 2006 (UTC)

• PM: pseudometric topology, id=6284 -- WP: pseudometric space -- Status: N

Mostly a proof, which is now referenced in the topology subsection of pseudometric space. linas 16:33, 22 November 2006 (UTC)

• PM: quasimetric space, id=6274 -- WP: quasimetric space -- Status: A

linas 06:46, 22 November 2006 (UTC)

• PM: sphere (metric space), id=6446^new! -- WP guess: sphere (metric space) -- Status:

• PM: totally bounded, id=3608^new! -- WP guess: totally bounded -- Status:

• PM: totally bounded subset of a metric space is bounded, id=7269^new! -- WP guess: totally bounded subset of a metric space is bounded -- Status:

• PM: ultrametric, id=4044^new! -- WP guess: ultrametric -- Status:

• PM: ultrametric space, id=6612^new! -- WP guess: ultrametric space -- Status:

• PM: uniform base, id=6498^new! -- WP guess: uniform base -- Status:

• PM: Urysohn metrization theorem, id=1531 -- WP: Urysohn metrization theorem -- Status: A

linas 19:29, 22 November 2006 (UTC)

[edit] 54E40 Special maps on metric spaces

• PM: near operators, id=5411 -- WP guess: near operators -- Status:

• PM: real tree, id=7071 -- WP: real tree -- Status: A

linas 22:12, 24 November 2006 (UTC)

[edit] 54E45 Compact (locally compact) metric spaces

• PM: Lebesgue number lemma, id=3402 -- WP guess: Lebesgue number lemma -- Status:

• PM: proof of Lebesgue number lemma, id=3596 -- WP guess: proof of Lebesgue number lemma -- Status:

• PM: Cantor's Intersection Theorem, id=6970^new! -- WP guess: Cantor's Intersection Theorem -- Status:

[edit] 54E50 Complete metric spaces

• PM: complete, id=603 -- WP guess: complete -- Status:

• PM: completeness principle, id=2171 -- WP guess: completeness principle -- Status:

• PM: nested sphere theorem, id=6648 -- WP guess: nested sphere theorem -- Status:

• PM: uniformly equicontinuous, id=3717 -- WP guess: uniformly equicontinuous -- Status:

• PM: Cantor space, id=4439^new! -- WP: Cantor space -- Status: A

Paul August ☎ 03:32, 27 August 2006 (UTC)

• PM: Polish space, id=6693^new! -- WP: Polish space -- Status: A

Paul August ☎ 03:28, 27 August 2006 (UTC)

[edit] 54E52 Baire category, Baire spaces

• PM: Baire category theorem, id=3024 -- WP guess: Baire category theorem -- Status:

• PM: Baire space, id=4342 -- WP: Baire space -- Status: A

linas 18:13, 19 November 2006 (UTC)

• PM: equivalent statement of Baire category theorem, id=5441 -- WP guess: equivalent statement of Baire category theorem -- Status:

• PM: generic, id=4341 -- WP guess: generic -- Status:

• PM: meager, id=3680 -- WP guess: meager -- Status:

• PM: proof for one equivalent statement of Baire category theorem, id=5442 -- WP guess: proof for one equivalent statement of Baire category theorem -- Status:

• PM: proof of Baire category theorem, id=3543 -- WP guess: proof of Baire category theorem -- Status:

• PM: residual, id=3476 -- WP guess: residual -- Status:

• PM: six consequences of Baire category theorem, id=5444 -- WP guess: six consequences of Baire category theorem -- Status:

• PM: \mathbb{R}^n is not a countable union of proper vector subspaces, id=6688^new! -- WP guess: \mathbbR^n is not a countable union of proper vector subspaces -- Status:

• PM: Banach spaces of infinite dimension don't have a countable algebraic basis, id=6691^new! -- WP guess: Banach spaces of infinite dimension don't have a countable algebraic basis -- Status:

• PM: no continuous function switches the rational and the irrational numbers, id=6692^new! -- WP guess: no continuous function switches the rational and the irrational numbers -- Status:

• PM: no countable dense subset of a complete metric space is a G_\delta, id=6689^new! -- WP guess: no countable dense subset of a complete metric space is a G_\delta -- Status:

• PM: there are continuous functions in the interval [0,1 which are not monotonic at any subinterval], id=6690^new! -- WP guess: [[there are continuous functions in the interval [0,1] which are not monotonic at any subinterval]] -- Status:

• PM: wiki dealing with Baire category theorem, id=7609^new! -- WP guess: wiki dealing with Baire category theorem -- Status:

[edit] 54E99 Miscellaneous

• PM: compactly generated, id=1688 -- WP: compactly generated space -- Status: A

Kompik 11:32, 22 February 2006 (UTC)

• PM: Hahn-Mazurkiewicz theorem, id=3369 -- WP: Hahn-Mazurkiewicz theorem -- Status: A

Paul August ☎ 03:13, 27 August 2006 (UTC)

• PM: Vitali covering, id=4072 -- WP guess: Vitali covering -- Status:

[edit] 54F45 Dimension theory

[edit] 54G05 Extremally disconnected spaces, $F$-spaces, etc.

• PM: extremally disconnected, id=2982 -- WP: extremally disconnected space -- Status: A

Paul August ☎ 03:20, 27 August 2006 (UTC)

[edit] 54G20 Counterexamples

• PM: Hedgehog space, id=6500 -- WP: Hedgehog space -- Status: C

linas 15:51, 19 November 2006 (UTC)

• PM: long line, id=4069 -- WP: long line (topology) -- Status: A

Paul August ☎ 02:58, 27 August 2006 (UTC)

• PM: Sierpinski space, id=1222 -- WP: Sierpinski space -- Status: A

Paul August ☎ 01:54, 27 August 2006 (UTC)

[edit] 54G99 Miscellaneous

[edit] 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)

[edit] 54H11 Topological groups

[edit] 54H13 Topological fields, rings, etc.

[edit] 54H20 Topological dynamics

[edit] 54H25 Fixed-point and coincidence theorems

[edit] 54H99 Miscellaneous