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An algorithm used to recursively construct a set of objects from the smallest possible constituent parts. Given a set of k integers (a_1, a_2, ..., a_k) with a_1<a_2<...<a_k, ...

A topological space is second countable if it has a countable topological basis.

In analysis, the phrase "Riesz-Fischer theorem" is used to describe a number of results concerning the convergence of Cauchy sequences in L-p spaces. The theorem is named for ...

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, ...

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 ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

A smooth manifold with a Poisson bracket defined on its function space.

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.