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Topic:
Cech Stone Compactification
Replies:
7
Last Post:
Jan 2, 2013 3:43 AM




Re: Cech Stone Compactification
Posted:
Dec 31, 2012 11:45 AM


On Mon, 31 Dec 2012 01:28:36 0800, William Elliot <marsh@panix.com> wrote:
>Would somebody elucidate what Wikipedia was saying about >StoneCech compactification? It doesn't make sense for >isn't a compactification an embedding into an compact space.
The StoneCech compactification is not a compactification, by the usual definitions.
> >Some authors add the assumption that the starting space be Tychonoff >(or even locally compact Hausdorff), for the following reasons: > * The map from X to its image in bX is a homeomorphism if and only > if X is Tychonoff. > * The map from X to its image in bX is a homeomorphism to an open > subspace if and only if X is locally compact Hausdorff. > >The StoneCech construction can be performed for more general spaces >X, but the map X > bX need not be a homeomorphism to the image of X >(and sometimes is not even injective).



