local compactness is hereditary for locally closed subspaces

Theorem - Let $X$ be a locally compact space and $Y\\subseteq X$ a subspace. If $Y$ is locally closed in $X$ then $Y$ is also locally compact.

The converse of this theorem is also true with the additional assumption that $X$ is Hausdorff.

Theorem 2 - Let $X$ be a locally compact Hausdorff space (http://planetmath.org/LocallyCompactHausdorffSpace) and $Y\\subseteq X$ a subspace. If $Y$ is locally compact then $Y$ is locally closed in $X$ .

单词	LocalCompactnessIsHereditaryForLocallyClosedSubspaces
释义	local compactness is hereditary for locally closed subspaces Theorem - Let $X$ be a locally compact space and $Y\\subseteq X$ a subspace. If $Y$ is locally closed in $X$ then $Y$ is also locally compact. The converse of this theorem is also true with the additional assumption that $X$ is Hausdorff. Theorem 2 - Let $X$ be a locally compact Hausdorff space (http://planetmath.org/LocallyCompactHausdorffSpace) and $Y\\subseteq X$ a subspace. If $Y$ is locally compact then $Y$ is locally closed in $X$ .
随便看	radical Radical1 Radical12 RadicalExtension radical extension RadicalOfAnIdeal radical of an ideal RadicalOfAnInteger radical of an integer RadicalTheory radical theory Radius radius RadiusOfConvergence radius of convergence RadiusOfConvergenceOfAComplexFunction radius of convergence of a complex function RadonMeasure Radon measure RadonNikodymTheorem Radon-Nikodym theorem RadonsLemma Radon’s lemma RadosTheorem Rado’s theorem