Definition:Cover of Set/Delta Cover

Definition
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 $\CC$ is a countable cover such that:
 * $\forall U \in \CC :0 < \size U \le \delta$

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