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#1 2010-05-06 07:24:21

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

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.

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#2 2010-05-11 07:48:21

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

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.

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#3 2010-05-13 07:06:29

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

Re: Tychonoff’s theorem

Oh, and Andrey Nikolayevich Tychonoff (1906–93) was a Russian mathematician.

http://z8.invisionfree.com/DYK/index.ph … &p=4451424 wink

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