Definition:Subcover

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Definition

Let $S$ be a set.

Let $\mathcal U$ be a cover for $S$.


A subcover of $\mathcal U$ for $S$ is a set $\mathcal V \subseteq \mathcal U$ such that $\mathcal V$ is also a cover for $S$.


Finite Subcover

A finite subcover of $\mathcal U$ for $S$ is a subcover $\mathcal V \subseteq \mathcal U$ which is finite.


Countable Subcover

A countable subcover of $\mathcal U$ for $S$ is a subcover $\mathcal V \subseteq \mathcal U$ which is countable.


Also see


Sources