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.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$