A Closure

Mathematics

Topology: A set is open if it does not contain any of its boundary points. It is left as an exercise to show that a set is open if and only if each of its points is an interior point. A set is closed if it contains all of its boundary points, and the closure of a set S is the closed set consisting of all points in S together with the boundary of S. Note that the first of sets is open and that the second is its closure.