Definition:Subcover
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Definition
Let $S$ be a set.
Let $\UU$ be a cover for $S$.
A subcover of $\UU$ for $S$ is a set $\VV \subseteq \UU$ such that $\VV$ is also a cover for $S$.
Finite Subcover
A finite subcover of $\UU$ for $S$ is a subcover $\VV \subseteq \UU$ which is finite.
Countable Subcover
A countable subcover of $\UU$ for $S$ is a subcover $\VV \subseteq \UU$ which is countable.
Also see
- Results about subcovers can be found here.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.2$: Definition of compactness: Definitions $5.2.1$