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:
“Alas! when Virtue sits high aloft on a frigate’s poop, when Virtue is crowned in the cabin of a Commodore, when Virtue rules by compulsion, and domineers over Vice as a slave, then Virtue, though her mandates be outwardly observed, bears little interior sway.”
—Herman Melville (1819–1891)