Topological interior

In topology, the interior of a set is the union of all open sets contained in it, and contains all interior points. It is the largest open set contained in the original set. The interior of a set S is denoted by int S, Int S, or, S^o.

A set S is an open set if and only if S is equal to the interior of S.

Examples

• The interior of the empty set is empty.
• int [1, 10] = (1, 10)
• int {(x, y) ∈ R² | y ∈ (0, 1]} = {(x, y) ∈ R² | y ∈ (0, 1)}