# Difference between revisions of "Closure (topology)"

Jump to navigation
Jump to search

imported>Hendra I. Nurdin m (Closure mathematical moved to Closure (mathematics): Closure (mathematics) reads better than Closure mathematical) |
imported>Hendra I. Nurdin m (link fix) |
||

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#Some topological notions|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 05:26, 22 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*.