Locally closed set
From Encyclopedia of Mathematics
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2020 Mathematics Subject Classification: Primary: 54B05 [MSN][ZBL]
in a topological space $X$
A subset of $X$ that is the intersection of an open set and a closed set in $X$: equivalently, a subset that is relatively open in its closure in $X$.
A submaximal space is one in which every subset is locally closed.
References
- Arhangel’skij, A.V.; Collins, P.J. On submaximal spaces Topology Appl. 64 (1995) 219-241 DOI 10.1016/0166-8641(94)00093-I Zbl 0826.54002
How to Cite This Entry:
Locally closed set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_closed_set&oldid=39774
Locally closed set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_closed_set&oldid=39774