locally closed
 A subset $Y$ of a topological space^{} $X$ is said to be locally closed if it is the intersection^{} of an open and a closed subset.
The following result provides some definitions:
 The following are equivalent^{}:

1.
$Y$ is locally closed in $X$.

2.
Each point in $Y$ has an open neighborhood $U\subseteq X$ such that $U\cap Y$ is closed in $U$ (with the subspace topology).

3.
$Y$ is open in its closure^{} $\overline{Y}$ (with the subspace topology).
Title  locally closed 

Canonical name  LocallyClosed 
Date of creation  20130322 17:36:12 
Last modified on  20130322 17:36:12 
Owner  asteroid (17536) 
Last modified by  asteroid (17536) 
Numerical id  5 
Author  asteroid (17536) 
Entry type  Definition 
Classification  msc 54D99 