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.

[0,1] \/ [2,3] is compact and has a big hole, (1,2).
(1,2) is an infinite process, ie (1,2) = \/_n (1+1/n, 1-1/n)
.