Meaning of Hausdorff space | Babel Free

Definitions

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.

Equivalents

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.”

“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.”

“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.”

CEFR level