Talk:Net (mathematics)

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Net stuff

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Explain why a directed set is used and a partial order is insufficient (the article on Preorder claims that general directed sets rather than partially ordered ones are necessary, but that is not explained either here or there). Dfeuer 20:13, 12 Aug 2004 (UTC) Figure out if I used the right terminology (should I have written cofinal rather than final?) Dfeuer 20:17, 12 Aug 2004 (UTC) Describe the different definitions that authors have used for nets. Dfeuer 20:17, 12 Aug 2004 (UTC) Describe the relationship between nets and filters, and why each is used in different circumstances. Dfeuer 20:17, 12 Aug 2004 (UTC) Prove that every net has a universal subnet. Dfeuer Give an example of a discontinuous function which is sequentially continuous. Lupin 15:26, 6 Sep 2004 (UTC)

Explain why a directed set is used and a partial order is insufficient (the article on Preorder claims that general directed sets rather than partially ordered ones are necessary, but that is not explained either here or there). Dfeuer 20:13, 12 Aug 2004 (UTC)
Figure out if I used the right terminology (should I have written cofinal rather than final?) Dfeuer 20:17, 12 Aug 2004 (UTC)
Describe the different definitions that authors have used for nets. Dfeuer 20:17, 12 Aug 2004 (UTC)
Describe the relationship between nets and filters, and why each is used in different circumstances. Dfeuer 20:17, 12 Aug 2004 (UTC)
Prove that every net has a universal subnet. Dfeuer
Give an example of a discontinuous function which is sequentially continuous. Lupin 15:26, 6 Sep 2004 (UTC)

1 Who is H. L. Smith?
2 Nets vs. Filters
3 Question
4 ε-nets
5 Nets vz. more general colimits

[edit] Who is H. L. Smith?

The original definition of nets appears in an article written by E. H. Moore and H. L. Smith. Who is the latter? My guess is Herman Lyle Smith, a PhD student of Moore according to the Mathematical Genealogy Project. Can anyone confirm this? -- Jitse Niesen 21:30, 26 Apr 2004 (UTC) Yes, Smith was Moore's student at University of Chicago. He went on to get a job at Louisiana State University and then dropped into obscurity. (See Halmos, Has progress in mathematics slowed down? American Mathematical Monthly, 97 (7), 1990.)

[edit] Nets vs. Filters

According to Kelley, the equivalence of nets and filters is part of the folklore of the subject. Is there a formal equivalence? If not, the statement here should be modified.

[edit] Question

Under examples, you wrote Then Xs is a net. Would not Then (Xs) is a net be a little clearer given the previous section?

[edit] ε-nets

This article is about nets in topological spaces and not about ε-nets in metric spaces

The link ε-net has nothing to do with ε-nets in metric spaces, but I wasn't able to find the correct one. --Kompik 12:13, 5 November 2005 (UTC)

[edit] Nets vz. more general colimits

Directed preorders, or directed sets or directed filters, appear much more generally than just in topology, in some definitions of direct limits. I would like to know if the usage of the term net with meanings close to the one in the article also is more widespread. JoergenB 18:04, 15 November 2007 (UTC)