On Mon, 31 Dec 2012 01:28:36 -0800, William Elliot <firstname.lastname@example.org> wrote:
>Would somebody elucidate what Wikipedia was saying about >Stone-Cech compactification? It doesn't make sense for >isn't a compactification an embedding into an compact space.
The Stone-Cech 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 Stone-Cech 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).