Category:Definitions/Hausdorff Metric

This category contains definitions related to Hausdorff Metric.
Related results can be found in Category:Hausdorff Metric.

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

Let $\CC$ be the set of compact subsets of $M$.

Let $\d: \CC \times \CC \to \R_{\ge 0}$ be the distance function on $M$ defined as:

$\forall A, B \in \CC: \map \d {A, B} :=$ the smallest $r \in \R_{\ge 0}$ such that $A$ and $B$ are each contained within the $r$-neighborhood of the other.

Then $\d$ is known as the Hausdorff metric on $M$.