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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Compactification
Replies: 15   Last Post: Mar 17, 2013 6:11 AM

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William Elliot

Posts: 644
Registered: 1/8/12
Re: Compactification
Posted: Dec 13, 2012 3:47 AM
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On Wed, 12 Dec 2012, Shmuel (Seymour J.) Metz wrote:
> In <Pine.NEB.4.64.1212112003320.6609@panix2.panix.com>, on 12/11/2012
> at 08:13 PM, William Elliot <marsh@panix.com> said:
>
> >Why the extra luggage of the embedding for the definition of
> >compactification? Why isn't the definition simply
> > Y is a compactification of X when there's some
> > embedding h:X -> Y for which h(X) is a dense subset of Y?
>
> Because in general there is more than one such imbedding.

So what? In general there's more than one element in a cofactor,
more that one cluster point of a sequence within a compact space.

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