Re: Topology Question

From: William Elliot <marsh@xxxxxxxxxxxxxxxxxx>
Date: Tue, 19 Apr 2005 18:10:32 -0700

On Tue, 19 Apr 2005, Zundark wrote:

> Martin Shobe wrote:
>
> > Is there a topology with unique sequential convergence on a
> > countable set thst is not Hausdorff?
>
> The one-point compactification of the rationals.

Are you sure? 1/n -> 0, but doesn't 1/n -> p the compactifying point?
If open U nhood p, then U = V \/ {p} for some cofinite V subset Q.
Thus eventually (1/n)_n subset U.

As I've previously pointed out, 1st countable US spaces are Hausdorff
and Q_p is 1st countable, is it not?

cf Space #35, Steen's "Counterexamples in Topology"e
.

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