Encyclopedia > Tychonoff theorem

  Article Content

Tychonoff's theorem

Redirected from Tychonoff theorem

Tychonoff's theorem in topology states that the product of any collection of compact topological spaces is compact.

For finite collections of compact spaces, this is not very surprising and is easy to prove. The statement is in fact true for infinite collections of arbitrary size, depends heavily on the peculiar definition of the product topology in this case, and is equivalent to the axiom of choice.

proof sketch would be nice



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Bolt action

... of the same. Typically, the capacity is around 5 rounds, as this permits the magazine to be completely flush with the bottom of the rifle, thus preserving ...