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mod07lec43 - Proof of Tychonoff's theorem - Part 1
Автор: NPTEL-NOC IITM
Загружено: 2022-03-07
Просмотров: 3452
Описание: We finally give a detailed proof of Tychonoff's theorem, using Zorn's Lemma in a fundamental way. As a Corollary, one obtains the fact that (1) a finite Cartesian product of compact spaces is compact, and (2) any closed and bounded subset of R^n is compact, since it is a closed subset of a product of compact intervals in R (which is then compact by (1). We note that both these points can be proved without the full force of Tychonoff's theorem, but here we give them as a corollary.
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