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


Sources