Closure (topology) - Closure Operator

See also:Closure operator

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

S− = X \ (X \ S)o

and also

So = X \ (X \ S)−

where X denotes 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.