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Hausdorff metrics

Hausdorff metrics is the plural of Hausdorff metric.

Meaning of Hausdorff metric

Noun

Hausdorff metric (plural Hausdorff metrics)

  1. In the abstract metric space of all compact subsets of ℝⁿ, given a pair of compact sets A and B, the Hausdorff metric is h(A,B)= mbox maxρ(A,B),ρ(B,A) where ρ(A,B)= sup _(a∈A) inf _(b∈B),d(a,b), where d is the Euclidean metric in ℝⁿ.
    • The Hausdorff metric topology was first discovered by D. Pompeiu and by F. Hausdorff in 1927. This topology has been used in a number of areas such as function space topologies, approximation theory, and optimisation (see, e.g., 22).2014, James F. Peters, Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces, Springer Science & Business Media, →ISBN, page 195
    Synonyms:
    Hausdorff distance, Pompeiu-Hausdorff distance

Questions about Hausdorff metrics

What is Hausdorff metrics the plural of?
Hausdorff metrics is the plural of Hausdorff metric.

Words near Hausdorff metrics in the dictionary

  1. Hausdorff distance
  2. Hausdorff distances
  3. Hausdorff gap
  4. Hausdorff gaps
  5. Hausdorff metric
  6. Hausdorff metrics
  7. Hausdorff space
  8. Hausdorff spaces
  9. Hausdorffness
  10. hause
  11. hausen

Source and license

Adapted from Wiktionary: Hausdorff metrics (page history and authors); Hausdorff metric (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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