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Topic: Compactifications
Replies: 6   Last Post: Mar 24, 2013 2:05 PM

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William Elliot

Posts: 1,608
Registered: 1/8/12
Re: Compactifications
Posted: Mar 23, 2013 10:16 PM
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On Sat, 23 Mar 2013, David C. Ullrich wrote:
> >> On Sat, 23 Mar 2013 00:30:27 -0700, William Elliot <marsh@panix.com>
> >> wrote:
> >>

> >> >Number of non-homeomophic n-point Hausdorff compactifications
> >> Compactifications of _what_?
> >
The space described at the beginning of each paragraph.

> >The reals x {0,1,...,k} I suppose.
>
> No, there's only one compactification of that set.


There's only one one-point compactification.
There are at least two two-pint compactifications:

the disjoint sum of a one-point compactificaiton of
Rx{0} and a one-point compactification of Rx{1,2,.. k}

a one-point p compactification of Rx{1,2,.. k} with
a closed unit interval one end of which is attached
to the compactifing point p.

> >>What the heck does that notation mean?
> >Too compact, is it?

:-}

> I'm going to pretend you didn't say that...




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