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 \( A \subseteq X \), \( A \subseteq C(A) \).