Main Page | See live article | Alphabetical index 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 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. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.