Definition:Cover of Set/Definition 2
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Definition
Let $S$ be a set.
A cover for $S$ is a set of sets $\CC$ such that:
- $\forall s \in S : \exists C \in \CC : x \in C$
Also known as
A cover is also known as a covering.
Also see
- Results about covers can be found here.
Sources
- 1955: John L. Kelley: General Topology: Chapter $1$: Topological Spaces, $\S$ Bases and Subbases
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cover
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cover