CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article is about boundaries in general topology . For the boundary of a manifold , see boundary of a manifold . This article includes a list of references , but its sources remain unclear because it has insufficient inline citations . Please help to improve this article by introducing more precise citations. (March 2013) ( Learn how and when to remove this template message ) A set (in light blue) and its boundary (in dark blue). In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S . More precisely, it is the set of points in the closure of S , not belonging to the interior of S . An element of the boundary of S is called a boundary point of S . The ...