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The boundary of a set in topology. The boundary operator on a chain complex in homological algebra. The boundary operator of a differential graded algebra. The conjugate of the Dolbeault operator on complex differential forms. The boundary ∂(S) of a set of vertices S in a graph is the set of edges leaving S, which defines a cut.
This concept has since been widely cited and the concept of a boundary object has been adopted in computer science (particularly computer supported cooperative work), information science, [4] and management, particularly when considering cross-disciplinary work and collaboration, [5] either within one organization or with the boundary object helping to focus the efforts of multiple organizations.
An object may be composed of components. A component is an object completely within the boundary of a containing object. A living thing may be an object, and is distinguished from non-living things by the designation of the latter as inanimate objects. Inanimate objects generally lack the capacity or desire to undertake actions, although humans ...
The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded. For example, a curve , such as a circle , is of dimension one, because the position of a point on a curve is determined by its signed distance along the curve to a fixed point on the ...
For example, the following would be considered Dirichlet boundary conditions: In mechanical engineering and civil engineering (beam theory), where one end of a beam is held at a fixed position in space. In heat transfer, where a surface is held at a fixed temperature. In electrostatics, where a node of a circuit is held at a fixed voltage.
A boundary point of a set is any element of that set's boundary. The boundary defined above is sometimes called the set's topological boundary to distinguish it from other similarly named notions such as the boundary of a manifold with boundary or the boundary of a manifold with corners, to name just a few examples.
Boundary representation has also been extended to allow special, non-solid model types called non-manifold models. As described by Braid, normal solids found in nature have the property that, at every point on the boundary, a small enough sphere around the point is divided into two pieces, one inside and one outside the object.
A Seifert surface of a knot is however a manifold with boundary, the boundary being the knot, i.e. homeomorphic to the unit circle. The genus of such a surface is defined to be the genus of the two-manifold, which is obtained by gluing the unit disk along the boundary.