In mathematics, specifically in general topology|topology, the interior of a set S of points of a topological space consists of all Topology glossary#P|points of S that do not belong to the Boundary_(topology)|boundary of S. A point that is in the interior of S is an interior point of S.
Equivalently the interior of S is the Absolute complement|complement of the closure (topology)|closure of the complement of S. In this sense interior and closure are Duality_(mathematics)#Duality_in_logic_and_set_theory|dual notions.The exterior of a set is the interior of its complement, equivalently the complement of its closure; it consists of the points that are in neither the set nor its boundary. The interior, boundary, and exterior of a subset together partition of a set|partition the whole space into three blocks (or fewer when one or more of these is empty). The interior and exterior are always open set|open while the boundary is always closed set|closed. Sets with empty interior have been called boundary sets.
In mathematics, specifically in general topology|topology, the interior of a set S of points of a topological space consists of all Topology glossary#P|points of S that do not belong to the Boundary_(topology)|boundary of S. A point that is in the interior of S is an interior point of S.
Equivalently the interior of S is the Absolute complement|complement of the closure (topology)|closure of the complement of S. In this sense interior and closure are Duality_(mathematics)#Duality_in_logic_and_set_theory|dual notions.The exterior of a set is the interior of its complement, equivalently the complement of its closure; it consists of the points that are in neither the set nor its boundary. The interior, boundary, and exterior of a subset together partition of a set|partition the whole space into three blocks (or fewer when one or more of these is empty). The interior and exterior are always open set|open while the boundary is always closed set|closed. Sets with empty interior have been...