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In mathematics, the interior of a subset A of a topological space X is the union of all open sets in X that are subsets of A. It is usually denoted by . It may equivalently be defined as the set of all points in A for which A is a neighbourhood.
- A set contains its interior, .
- The interior of a open set G is just G itself, .
- Interior is idempotent: .
- Interior distributes over finite intersection: .
- 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.