Definition:Cover of Set/Finite

Definition

Let $S$ be a set.

A cover $\CC$ for $S$ is a finite cover if and only if $\CC$ is a finite set.

Illustration

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

Also see

• Results about covers can be found here.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.2$: Definition of compactness: Definitions $5.2.1$