locally compact Hausdorff space
GPTKB entity
Statements (50)
| 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 |
| 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:Tychonoff_space
gptkb:Alexandroff_compactification |
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
locally compact Hausdorff space
|