Definition:Cover of Set/Subset

Definition

Let $S$ be a set.

Let $T \subseteq S$ be a subset.

Let $\CC$ be a set of subsets of $S$.

Then $\CC$ is a cover of $T$ if and only if $T \subseteq \ds \bigcup \CC$, where $\cup$ denotes union.

Illustration

The following diagram illustrates a cover of a subset $T$ of a set $S$:

Also see

• Definition:Open Cover of Subset

Sources

• 2009: W.A. Sutherland: Introduction to Metric and Topological Spaces (2nd ed.): $13$: Compact spaces $\S$ Definition of compactness: Definition $13.3$