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.