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

[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.