# Locally closed set

From Encyclopedia of Mathematics

2010 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