Metric Space Induced by Hausdorff Metric

Theorem

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 Hausdorff metric on $\CC$.

Then $\struct {\CC, \d}$ is a metric space.

Proof

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Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hausdorff metric