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#1 2010-05-07 05:24:21
- JaneFairfax
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Tychonoff’s theorem
Tychonoff’s theorem: http://z8.invisionfree.com/DYK/index.php?showtopic=900
Tychonoff’s theorem has applications in modern analysis. It is also used to prove the Heine–Borel theorem, namely that all closed and bounded subspaces of are compact.
#2 2010-05-12 05:48:21
- JaneFairfax
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Re: Tychonoff’s theorem
More about Tychonoff’s theorem.
Tychonoff’s theorem in the infinite case is equivalent to the axiom of choice. The converse to Tychonoff’s theorem is also true because if is compact, then each , being a continous projection of , must be compact as well.
#3 2010-05-14 05:06:29
- JaneFairfax
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Re: Tychonoff’s theorem
Oh, and Andrey Nikolayevich Tychonoff (1906–93) was a Russian mathematician.
http://z8.invisionfree.com/DYK/index.ph … ;p=4451424 