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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Tychonoffs theorem: http://z8.invisionfree.com/DYK/index.php?showtopic=900

Tychonoffs theorem has applications in modern analysis. It is also used to prove the HeineBorel theorem, namely that all closed and bounded subspaces of are compact.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

More about Tychonoffs theorem.

Tychonoffs theorem in the infinite case is equivalent to the axiom of choice. The converse to Tychonoffs theorem is also true because if is compact, then each , being a continous projection of , must be compact as well.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Oh, and Andrey Nikolayevich Tychonoff (190693) was a Russian mathematician.

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