Interior (topology)
In mathematics, specifically in topology, the interior of a set S of points of a topological space 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.
Equivalently the interior of S is the complement of the closure of the complement of S. In this sense interior and closure are 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 the whole space into three blocks (or fewer when one or more of these is empty). The interior and exterior are always open while the boundary is always closed. Sets with empty interior have been called boundary sets.
Read more about Interior (topology): Examples, Interior Operator, Exterior of A Set
Famous quotes containing the word interior:
“The work of art, just like any fragment of human life considered in its deepest meaning, seems to me devoid of value if it does not offer the hardness, the rigidity, the regularity, the luster on every interior and exterior facet, of the crystal.”
—André Breton (1896–1966)