Locally closed set

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