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Hausdorff spaces

Hausdorff spaces is the plural of Hausdorff space.

Meaning of Hausdorff space

Noun

Hausdorff space (plural Hausdorff spaces)

  1. A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that x∈U and y∈V.
    • More generally, each compact subset of a Hausdorff space is closed.[…]Metric spaces and compact Hausdorff spaces enjoy an even stronger separation property; in either case, disjoint closed sets can always be separated by disjoint open sets.2005, N. L. Carothers, A Short Course on Banach Space Theory, Cambridge University Press, page 167
    Synonyms:
    T₂ space

Questions about Hausdorff spaces

What is Hausdorff spaces the plural of?
Hausdorff spaces is the plural of Hausdorff space.

Words near Hausdorff spaces in the dictionary

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

Source and license

Adapted from Wiktionary: Hausdorff spaces (page history and authors); Hausdorff space (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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