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.
- A set is contained in its closure, .
- The closure of a closed set F is just F itself, .
- Closure is idempotent: .
- Closure distributes over finite union: .
- The complement of the closure of a set in X is the interior of the complement of that set; the complement of the interior of a set in X is the closure of the complement of that set.