local compactness is hereditary for locally closed subspaces
Theorem - Let be a locally compact space and a subspace. If is locally closed in then is also locally compact.
The converse of this theorem is also true with the additional assumption that is Hausdorff.
Theorem 2 - Let be a locally compact Hausdorff space (http://planetmath.org/LocallyCompactHausdorffSpace) and a subspace. If is locally compact then is locally closed in .
Title | local compactness is hereditary for locally closed subspaces |
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Canonical name | LocalCompactnessIsHereditaryForLocallyClosedSubspaces |
Date of creation | 2013-03-22 17:36:33 |
Last modified on | 2013-03-22 17:36:33 |
Owner | asteroid (17536) |
Last modified by | asteroid (17536) |
Numerical id | 5 |
Author | asteroid (17536) |
Entry type | Theorem |
Classification | msc 54D45 |
Related topic | LocallyCompactHausdorffSpace |