Difference between revisions of "Closure (topology)"

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imported>Jitse Niesen
m (subject/verb agreement)
imported>Hendra I. Nurdin
m (emboldened 'closure')
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In [[mathematics]], the ''closure'' of a subset ''A'' of a [[topological space]] ''X'' is the set union of ''A'' and ''all'' its [[topological space|limit points]] in ''X''. It is usually denoted by <math>\overline{A}</math>. Other equivalent definitions of the closure of A are as the smallest [[closed set]] in ''X'' containing ''A'', or the intersection of all closed sets in ''X'' containing ''A''.  
In [[mathematics]], the '''closure''' of a subset ''A'' of a [[topological space]] ''X'' is the set union of ''A'' and ''all'' its [[topological space|limit points]] in ''X''. It is usually denoted by <math>\overline{A}</math>. Other equivalent definitions of the closure of A are as the smallest [[closed set]] in ''X'' containing ''A'', or the intersection of all closed sets in ''X'' containing ''A''.  


[[Category:Mathematics_Workgroup]]
[[Category:Mathematics_Workgroup]]
[[Category:CZ Live]]
[[Category:CZ Live]]

Revision as of 00:30, 17 September 2007

In mathematics, the closure of a subset A of a topological space X is the set union of A and all its limit points in X. It is usually denoted by . Other equivalent definitions of the closure of A are as the smallest closed set in X containing A, or the intersection of all closed sets in X containing A.