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Hausdorff distance

For nonempty bounded subsets of a metric space,

d_{H} (A, B) = max {sup_{a \in A} d (a, B), sup_{b \in B} d (b, A)} .

This is a metric on the nonempty closed bounded subsets. Without closedness it is only a pseudometric: a set and its closure have distance zero.

Table of contents 101 2
- Closed singleton embedding in a Hausdorff hyperspace Hausdorff distance 62 1
  - Completeness is reflected by the Hausdorff hyperspace Closed singleton embedding in a Hausdorff hyperspace 30

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