Interior (topology)
![The point x is an interior point of S. The point y is on the boundary of S.](/Images/godic/202501/20/Interior_illustration.svg4126.png")
![The red shapes are not interior-disjoint the blue Triangle. The green and the yellow shapes are interior-disjoint with the blue Triangle, but only the yellow shape is entirely disjoint from the blue Triangle.](/Images/godic/202501/20/Interior-disjoint.svg4126.png")
In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S.
The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.