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Boundary
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Boundary

''Ths article is about the geometric concept. For boundaries in the sport of cricket, see Boundary (cricket).


A boundary encloses a region of space, a territory, and/or an area. Something enclosed by a boundary, is "bounded" (by the boundary).

See also border.

An alternate meaning for boundary can be a psychological, physical or mental place which we keep between ourselves and others. Sometimes this can be referred to as personal space. Addicts use boundaries to keep themselves sober. Some times these may be called bottom lines.

See also bottom line behaviour.


In topology and related fields, the boundary of a subset is the set of all points of that space in its closure that are not interior points. More precisely, the boundary of a subset S is the difference between its closure and its interior. The boundary is always a closed set.

On the other hand, a manifold with boundary means something like a manifold, but modelled on a half-Euclidean space, on one side of a hyperplane. If the boundary points are removed an open subset that is a genuine manifold remains. The boundaries of manifolds are important, for example, in Stokes' theorem, and cobordism theory.

See also compactification.