proof of Tychonoff’s theorem in finite case
To prove that is compact if the are compact, it suffices (by induction) to prove that is compact when and are. It also suffices to prove that a finite subcover can be extracted from every open cover of by only the basis sets of the form , where is open in and is open in .
The proof is by the straightforward strategy of composing a finite subcover from a lower-dimensional subcover. Let the open cover of by basis sets be given.
|Title||proof of Tychonoff’s theorem in finite case|
|Date of creation||2013-03-22 15:26:27|
|Last modified on||2013-03-22 15:26:27|
|Last modified by||stevecheng (10074)|