# Thread: Compact sets and covers

1. ## Compact sets and covers

If you have a topological space that is compact, is it a cover itself?

If so, how to prove this?

2. What do you mean by "it is a cover itself" ?

3. 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?

4. 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.

5. 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.

6. Just wanted to make sure, thank you :]