Wikipedia:WikiProject Mathematics/PlanetMath Exchange/52-XX Convex and discrete geometry

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52-XX Convex and discrete geometry.

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[edit] 52-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: convex analysis, id=6954 -- WP guess: convex analysis -- Status:

[edit] 52A01 Axiomatic and generalized convexity

• PM: convex combination, id=401 -- WP: convex combination -- Status: A

Or one might want to copy some formulae, in addition to a verbal description. Mikkalai 02:47, 14 Feb 2005 (UTC)

[edit] 52A07 Convex sets in topological vector spaces

• PM: Fréchet space, id=3528 -- WP: Fréchet space -- Status: A

Unless someone wants to add proofs (which is IMO not really necessary in encyclopedia) Mikkalai 02:50, 14 Feb 2005 (UTC)

• PM: recession cone, id=8471^new! -- WP guess: recession cone -- Status:

[edit] 52A15 Convex sets in $3$ dimensions (including convex surfaces)

[edit] 52A20 Convex sets in $n$ dimensions (including convex hypersurfaces)

• PM: Carathéodory's theorem, id=4730 -- WP: Carathéodory's theorem (convex hull) -- Status: A

Mikkalai 03:38, 14 Feb 2005 (UTC)

• PM: proper cone, id=6199 -- WP : proper cone -- Status: M

Merged into Cone (geometry), and proper cone redirects thereMikkalai 03:38, 14 Feb 2005 (UTC)

Renamed cone (geometry) to cone (linear algebra). Jorge Stolfi 03:26, 23 December 2005 (UTC)

• PM: Radon's lemma, id=4710 -- WP : Radon's lemma -- Status: C

Jtwdog 21:16, 28 October 2005 (UTC)

[edit] 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)

• PM: Wulff Theorem, id=7144 -- WP guess: Wulff Theorem -- Status:

[edit] 52A30 Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)

[edit] 52A35 Helly-type theorems and geometric transversal theory

• PM: Helly's theorem, id=4728 -- WP: Helly's theorem -- Status: A

Note: PM proof is much shorter, whatever this may mean. User:Mikkalai 15:30, 3 February 2005 (UTC)

[edit] 52A41 Convex functions and convex programs

[edit] 52A99 Miscellaneous

• PM: convex set, id=243 -- WP : convex set -- Status: A

Mikkalai 03:51, 14 Feb 2005 (UTC)

• PM: extreme point, id=5920 -- WP : extreme point -- Status: A

Mikkalai 03:51, 14 Feb 2005 (UTC)

• PM: if A is convex and f linear then f(A) and f^{-1}(A) are convex, id=6175 -- WP guess: if A is convex and f linear then f(A) and f^-1(A) are convex -- Status: N

Nameless proposition. Mikkalai 03:51, 14 Feb 2005 (UTC)

• PM: internal point, id=5923 -- WP : internal point -- Status: NC

Mikkalai 03:51, 14 Feb 2005 (UTC)

• PM: extreme subset of convex set, id=7252 -- WP guess: extreme subset of convex set -- Status:

• PM: proof of properties of extreme subsets of a closed convex set, id=7264 -- WP guess: proof of properties of extreme subsets of a closed convex set -- Status:

• PM: properties of extreme subsets of a closed convex set, id=7253 -- WP guess: properties of extreme subsets of a closed convex set -- Status:

• PM: face of a convex set, id=8530^new! -- WP guess: face of a convex set -- Status:

• PM: alternative definition of face of a convex set, id=9320^new! -- WP guess: alternative definition of face of a convex set -- Status:

[edit] 52Axx General convexity

[edit] 52B05 Combinatorial properties (number of faces, shortest paths, etc.)

• PM: embedding, id=7385 -- WP guess: embedding -- Status:

[edit] 52B11 $n$-dimensional polytopes

• PM: isothetic, id=7912^new! -- WP guess: isothetic -- Status:

[edit] 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)

• PM: polytope, id=5544 -- WP: Convex polytope -- Status: NM

Jtwdog 21:21, 28 October 2005 (UTC)

• PM: f-vector, id=9264^new! -- WP guess: f-vector -- Status:

• PM: Weyl-Minkowski theorem, id=9262^new! -- WP guess: Weyl-Minkowski theorem -- Status:

[edit] 52B45 Dissections and valuations (Hilbert's third problem, etc.)

[edit] 52B99 Miscellaneous

• PM: pure simplicial complex, id=5780 -- WP: pure simplicial complex -- Status: A

Redirect to simplicial complex Mikkalai 00:19, 11 Feb 2005 (UTC)

• PM: hyperplane arrangement, id=7760^new! -- WP guess: hyperplane arrangement -- Status:

• PM: intersection semilattice of a subspace arrangement, id=7761^new! -- WP guess: intersection semilattice of a subspace arrangement -- Status:

• PM: zonotope, id=7749^new! -- WP guess: zonotope -- Status:

[edit] 52Bxx Polytopes and polyhedra

[edit] 52C07 Lattices and convex bodies in $n$ dimensions

[edit] 52C10 Erdös problems and related topics of discrete geometry

[edit] 52C35 Arrangements of points, flats, hyperplanes

• PM: K-distance set, id=5788 -- WP : K-distance set -- Status: NC

Mikkalai 05:12, 14 Feb 2005 (UTC)

[edit] 52Cxx Discrete geometry