Definition:Cover of Set/Subset
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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
Sources
- 2009: W.A. Sutherland: Introduction to Metric and Topological Spaces (2nd ed.): $13$: Compact spaces $\S$ Definition of compactness: Definition $13.3$