Definition:Open Cover/Subset
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Definition
Let $\struct {S, \tau}$ be a topological space.
Let $H$ be a subset of $S$.
Let $\CC$ be a cover of $H$.
Then $\CC$ is an open cover for $H$ if and only if:
- $\CC \subseteq \tau$
That is, if and only if all the elements of $\CC$ are open sets.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.2$: Definition of compactness: Definitions $5.2.1$
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis: Chapter $1$: Normed and Banach spaces