# Compact sets and covers

• Jun 1st 2011, 09:01 AM
Borkborkmath
Compact sets and covers
If you have a topological space that is compact, is it a cover itself?

If so, how to prove this?
• Jun 1st 2011, 09:03 AM
girdav
What do you mean by "it is a cover itself" ?
• Jun 1st 2011, 09:13 AM
Plato
Quote:

Originally Posted by Borkborkmath
If you have a topological space that is compact, is it a cover itself?
If so, how to prove this?

$\displaystyle (X,\mathcal{T})$ is a topological space is $\displaystyle X$ a basic open set?
• Jun 1st 2011, 01:12 PM
Borkborkmath
Yeah, sorry for the poor wording.
I was wondering if (X,tau) was a topological space if X was a cover of (X,tau). Or as plato said.
• Jun 1st 2011, 01:21 PM
Plato
Quote:

Originally Posted by Borkborkmath
Yeah, sorry for the poor wording.
I was wondering if (X,tau) was a topological space if X was a cover of (X,tau). Or as plato said.

In any topology space $\displaystyle (X,\tau)$, yes $\displaystyle X$ is an open cover of itself. That fact is true if the space is compact or not compact. So what is the point?
Please tell us what you are going for.
• Jun 2nd 2011, 10:14 AM
Borkborkmath
Just wanted to make sure, thank you :]