Is X a cover of itself?

Question

For a topological space $(X, F)$ where $X$ is the set of all elements and F the set of open sets, is $\{X\}$ a cover of the space?

Answer 1

Does each point $p\in X $ has an open set of your collection $\{X\}$? Yes, because $X$ itself is open, as of the topology definition. So the collection is an open cover.

The tag is weird. A covering space is not an open cover.