Difference between revisions of "Locally closed set"
From Encyclopedia of Mathematics
(Start article: Locally closed set) |
(define submaximal, cite Arhangel’skij and Collins) |
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''in a [[topological space]] $X$'' | ''in a [[topological space]] $X$'' | ||
| − | A subset of $X$ that is the intersection of an [[open set]] and a [[closed set]] in $X$. | + | 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 (-closed) set|relatively open]] in its closure in $X$. |
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| + | A '''submaximal space''' is one in which every subset is locally closed. | ||
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| + | ====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}} | ||
Latest revision as of 18:35, 19 November 2016
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=37245
Locally closed set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_closed_set&oldid=37245