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In [[topology]], the '''boundary''' of a [[set]] ''X'' is the [[intersection]] of the [[closure]] of ''X'' and the closure of the [[complement]] of ''X''.  

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 set]]s 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]].

Every set has a boundary, but only [[closed set]]s 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. Depending on the context, boundaries can be referred to by more common names: [[perimeter]], [[surface]], [[frontier]], [[border]], and [[edge]].

[[category:topology]]

[[category:topology]]