locally compact Hausdorff space

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:topology
gptkbp:characterizedBy	Hausdorff separation axiom every point has a compact neighborhood
gptkbp:definedIn	a topological space that is both locally compact and Hausdorff
gptkbp:example	gptkb:Euclidean_space real line locally compact group finite-dimensional manifolds discrete space
gptkbp:hasNonExample	infinite-dimensional Hilbert space (with weak topology)
gptkbp:hasProperty	gptkb:Hausdorff locally compact
gptkbp:hasSubgroup	Hausdorff space locally compact space
https://www.w3.org/2000/01/rdf-schema#label	locally compact Hausdorff space
gptkbp:importantFor	gptkb:Stone–Čech_compactification gptkb:Tychonoff_theorem gptkb:Urysohn's_lemma gptkb:Riesz_representation_theorem gptkb:Pontryagin_duality gptkb:one-point_compactification theory of C*-algebras existence of regular Borel measures
gptkbp:isClosedUnder	taking closed subsets taking finite products taking open subsets
gptkbp:isNotClosedUnder	quotients arbitrary products
gptkbp:relatedTo	gptkb:T2_space gptkb:Polish_space gptkb:Baire_space gptkb:Tychonoff_space Hausdorff space compact space locally compact space metrizable space second-countable space paracompact space normal space regular space locally compact group completely regular space sigma-compact space
gptkbp:usedIn	gptkb:topology functional analysis harmonic analysis measure theory
gptkbp:bfsParent	gptkb:Baire_space gptkb:Tychonoff_space gptkb:Alexandroff_compactification gptkb:Locally_compact_groups
gptkbp:bfsLayer	7