# Closure (topology): Difference between revisions

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imported>Hendra I. Nurdin |
imported>Jitse Niesen m (subject/verb agreement) |
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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 | 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 22:26, 16 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*.