Closure (topology): Difference between revisions
Jump to navigation
Jump to search
imported>Jitse Niesen m (subject/verb agreement) |
imported>Hendra I. Nurdin m (emboldened 'closure') |
||
| Line 1: | Line 1: | ||
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 23:30, 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.
