Boundary
This is an old revision of this page, as edited by Foxtrot (talk | contribs) at 05:15, May 29, 2008. It may differ significantly from current revision.
In topology, the boundary of a set X is the intersection of the closure of X and the closure of the complement of X.
Every set has a boundary, but only closed sets contain their boundaries. In contrast, an open set never contains its boundary. Example: both [0,1] and (0,1) have the boundary {0,1}. The first set is closed and contains its boundary; the second set is open and does not contain its boundary. Boundaries go under the more common names: perimeter, surface, frontier, and edge.