Re: Compactness

On Sun, 3 Dec 2006, Saurav wrote:

I heard that the defn of compactness by filter basis of closed sets,
or the convergence of ultrafilters, is related to the following in some
way, which

I don't know:
Compactness of anything, not only of topological spaces, means " it is
without holes",
where holes are infinite process without end.

Kindly explain if there is at all such concepts, and if there is,
explain it.

A space S is compact iff
every open cover of S has a finite subcover
every filter on S has a cluster point
every ultra filter on S converges.

.

Relevant Pages

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  • Compactness
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