Interior (topology) - Interior Operator

The interior operator o is dual to the closure operator —, in the sense that

So = X \ (X \ S)—,

and also

S— = X \ (X \ S)o

where X is the topological space containing S, and the backslash refers to the set-theoretic difference.

Therefore, the abstract theory of closure operators and the Kuratowski closure axioms can be easily translated into the language of interior operators, by replacing sets with their complements.