KnowraHausdorff spaceLinked fromLinked fromThe 17 pages that link to Hausdorff space, each with the reason it gives.All 17Broader topic 3Related 9Compared with 5Compact spaceRelated: Compact subsets of Hausdorff spaces are closed, a useful consequence requiring this extra axiom.HomeomorphismRelated: The Hausdorff condition makes compact-to-Hausdorff continuous bijections automatically homeomorphisms.Stone–Čech compactificationRelated: The compactification and its universal target spaces are required to be Hausdorff.Convergent sequenceRelated: The Hausdorff separation property ensures that convergent sequences have unique limits.Sequential compactnessRelated: Hausdorffness ensures sequence limits are unique, though it is not required by the definition.Urysohn's metrization theoremRelated: The theorem’s regularity hypothesis entails point separation in the standard T1 setting.Pavel AlexandrovRelated: The one-point compactification has its standard form for locally compact Hausdorff spaces.Cantor's intersection theoremRelated: Hausdorffness helps distinguish compact-set formulations from stronger uniqueness claims.Stone's representation theorem for Boolean algebrasRelated: The theorem's representing space separates distinct ultrafilters by neighborhoods.