Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Login

Username

Password

Not registered yet?

#1 2010-05-07 05:24:21

JaneFairfax
Legendary Member

Offline

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.


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#2 2010-05-12 05:48:21

JaneFairfax
Legendary Member

Offline

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.


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#3 2010-05-14 05:06:29

JaneFairfax
Legendary Member

Offline

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


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

Board footer

Powered by FluxBB