Definition:Cover of Set
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Let $S$ be a set.
A cover for $S$ is a set of sets $\CC$ such that:
- $\displaystyle S \subseteq \bigcup \CC$
where $\bigcup \CC$ denotes the union of $\CC$.
We say that $S$ is covered by $\CC$.
Let $A \subseteq S$ be a subset.
Also known as
A cover is also known as a covering.
- Results about covers can be found here.
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5.2$: 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): Entry: cover