Definition:Cover of Set

Definition
Let $S$ be a set.

A cover for $S$ is a set of sets $\mathcal C$ such that:
 * $\displaystyle S \subseteq \bigcup \mathcal C$

where $\bigcup \mathcal C$ denotes the union of $\mathcal C$.

We say that $S$ is covered by $\mathcal C$.

Also known as
A cover is also known as a covering.

Also see

 * Definition:Open Cover