Re: compact groups and AC

On Sun, 24 Jul 2005, Stephen J. Herschkorn wrote:

> G. A. Edgar wrote:
>
> >Another point here.
> >How do you define "compact"? Since there are many equivalent
> >definitions, but the equivalence requires AC, this is important.
> >
>
> Any open cover has a finite subcover. To what other definitions do you
> refer?
>
The DeMorgan or complement dual definition?

for any collection of closed sets with empty intersection,
there is a finite subcollection with empty intersection
or
the intersection of any collection of closed sets with fip, isn't empty.

fip means finite intersection property
every finite subcollection has non empty intersection.
.

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