Definition:Cover of Set/Delta Cover

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Let $S$ be a set.

Let $\struct {S, d}$ be a metric space.

Let $\delta \in \R_{>0}$.

A cover $\CC$ for $S$ is a $\delta$-cover if and only if $\CC$ is a countable cover such that:

$\forall U \in \CC :0 < \size U \le \delta$

where $\size U$ denotes the diameter of $U$.

Also see

  • Results about covers can be found here.