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Difference between revisions of "Locally closed set"

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(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 $X$.
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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====
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* 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

How to Cite This Entry:
Locally closed set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_closed_set&oldid=39774