Hausdorff space

plural Hausdorff spaces

1. mathematicsA 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.

   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.

   2012, Neil Hindman, Dona Strauss, Algebra in the Stone-Cech Compactification: Theory and Applications, 2nd edition, Walter de Gruyter, page 83

   2 more examples

   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

   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.

   2008, Thiruvaiyaru V. Panchapagesan, The Bartle-Dunford-Schwartz Integral, Springer (Birkhäuser), page ix

   Synonyms: T₂ space