Source: wikibot/closure-operator
= Closure operator
{wiki=Closure_operator}
In mathematics, particularly in the fields of topology, algebra, and lattice theory, a **closure operator** is a function that assigns a subset (the closure) to every subset of a given set, satisfying certain axioms. A closure operator \\( C \\) on a set \\( X \\) must satisfy the following three properties: 1. **Extensiveness**: For every subset \\( A \\subseteq X \\), \\( A \\subseteq C(A) \\).