Definition:Open Cover

Definition
Let $$T$$ be a topological space.

Let $$X$$ be some subset of $$T$$.

Then an open cover of $$X$$ is any collection $$C$$ of open sets of $$T$$ such that $$C$$ is a cover of $$T$$.

In particular, $$X$$ may equal $$T$$ in this definition.