Definition:Cover of Set/Delta Cover
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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 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.
Sources
- 2014: Kenneth Falconer: Fractal Geometry: Mathematical Foundations and Applications (3rd ed.): $3.1$ Hausdorff measure