Definition:Entropy of Open Cover

Definition
Let $X$ be a topological Space.

Let $\alpha$ be an open cover of $X$.

The entropy of $\alpha$ is defined as:
 * $\map H \alpha := \log \map N \alpha$

where:
 * $\ds \map N \alpha := \min \leftset {\card \beta : \beta}$ is a subcover of $\ds \rightset \alpha$
 * $\card \cdot$ denotes the cardinality