Boundary Point of a Set

a point each of whose neighborhoods contains points of the set as well as points not in the set. The set of all boundary points of a set forms its boundary. In the case of open sets, that is, sets in which each point has a neighborhood contained within the set, the boundary points do not belong to the set. Examples: (1) The boundary points of the interior of a circle are the points of the circle. (2) The points in space not on a given line form a region for which all points of the line are boundary points: the line is the boundary of the region.