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Hausdorff metric

Hausdorff metric noun: 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.

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

Synonyms of Hausdorff metric

Forms of Hausdorff metric

pluralHausdorff metrics

Questions about Hausdorff metric

What does Hausdorff metric mean?
Hausdorff metric means 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.
What part of speech is Hausdorff metric?
Hausdorff metric is a noun.
What is the plural of Hausdorff metric?
The plural of Hausdorff metric is Hausdorff metrics.

Words near Hausdorff metric in the dictionary

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

Source and license

Adapted from Wiktionary: 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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