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A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

Let X be an arbitrary topological space. Denote the set closure of a subset A of X by A^- and the complement of A by A^'. Then at most 14 different sets can be derived from A ...

Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function psi(x), sometimes ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...

A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers. The term is also used to refer to a regular ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...