Definition:Cover of Set/Definition 1

Definition

Let $S$ be a set.

A cover of (or for) $S$ is a set of sets $\CC$ such that:

$\ds S \subseteq \bigcup \CC$

where $\bigcup \CC$ denotes the union of $\CC$.

Also known as

A cover is also known as a covering.

Also see

• Equivalence of Definitions of Cover of Set

• Results about covers can be found here.

Sources

• 1955: John L. Kelley: General Topology: Chapter $1$: Topological Spaces, $\S$ Bases and Subbases
• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.2$: Definition of compactness: Definitions $5.2.1$
• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): cover