Changes

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 ''A''. It is a [[function]] ''cl'' from ''A'' to the [[power set]] of ''A'' satisfying the following conditions:

* <math>A\in cl(A)</math> (augmentation)

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

* If <math>B\subset A</math> then <math>cl(B)\subset cl(A)</math> (monotonicity)

* If <math>B\subset A</math> then <math>cl(B)\subset cl(A)</math> ([[Monotone|monotonicity]])

* <math>cl(A)\in cl(A)</math> (idempotence)

* <math>cl(A)\in cl(A)</math> ([[idempotent|idempotence]])

In the category of [[topological space]]s, this operator is isomorphic to the standard topological one.

In the category of [[topological space]]s, this operator is isomorphic to the standard topological one.

[[Category:Topology]]

[[Category:Topology]]