Changes

In [[topology]], the '''closure''' of a set ''A'' is the intersection of all [[closed set]]s containing ''A''. In [[metric space]]s, this can be also defined as the set of all [[limit point]]s of the set ''A''.

In [[topology]], the '''closure''' of a set <math>A</math> is the intersection of all [[closed set]]s containing <math>A</math>. Equivalently, the closure of <math>A</math> is the union of <math>A</math> and all [[limit point]]s of <math>A</math>

A '''closure operator''' is an abstract ([[category theory]]) form of the topological notion of closure which can be applied to any set ''A''. It is a [[function]] ''cl'' from ''A'' to the [[power set]] of ''A'' satisfying the following conditions:

A '''closure operator''' is an abstract ([[category theory]]) form of the topological notion of closure which can be applied to any set <math>A</math>. It is a [[function]] <math>cl</math> from <math>A</math> to the [[power set]] of <math>A</math> satisfying the following conditions:

* <math>A\in cl(A)</math> ([[augment]]ation)

* <math>A\in cl(A)</math> ([[augment]]ation)