Hausdorff space

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English

English Wikipedia has an article on:

Hausdorff space

Etymology

Named after German mathematician Felix Hausdorff (1868–1942).

Noun

Hausdorff space (plural Hausdorff spaces)

(topology) 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 $x\in U$ $x\in U$ and $y\in V$ $y\in V$ .
- 2005, N. L. Carothers, A Short Course on Banach Space Theory, Cambridge University Press, page 167:
  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.
- 2008, Thiruvaiyaru V. Panchapagesan, The Bartle-Dunford-Schwartz Integral‎, Springer (Birkhäuser), page ix:
  In 1953, Grothendieck [G] characterized locally convex Hausdorff spaces which have the Dunford-Pettis property and used this property to characterize weakly compact operators u : C(K) → F, where K is a compact Hausdorff space and F is a locally compact Hausdorff space (briefly, lcHs) which is complete.
- 2012, Neil Hindman, Dona Strauss, Algebra in the Stone-Cech Compactification: Theory and Applications, 2nd edition, Walter de Gruyter, page 83:
  Our construction of βD is a special case of more general constructions in which compact Hausdorff spaces are obtained using sets which are maximal subject to having certain algebraic properties.

Synonyms

(topological space in which distinct points are contained in distinct open sets): T₂ space

Hypernyms

sober space
- topological space

Hyponyms

Translations

Translations

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