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One of the Eilenberg-Steenrod axioms. Let X be a single point space. H_n(X)=0 unless n=0, in which case H_0(X)=G where G are some groups. The H_0 are called the coefficients ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

A diminished polyhedron is a polyhedron in which one or more groups of associated faces (such as those comprising the top of a pyramid or cupola in the case of a Johnson ...

An expansion based on the roots of x^(-n)[xJ_n^'(x)+HJ_n(x)]=0, where J_n(x) is a Bessel function of the first kind, is called a Dini expansion.

A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

Characterized by allowing only integer values.

A set S of positive integers is said to be Diophantine iff there exists a polynomial Q with integral coefficients in m>=1 indeterminates such that ...

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

If (f,U) and (g,V) are functions elements, then (g,V) is a direct analytic continuation of (f,U) if U intersection V!=emptyset and f and g are equal on U intersection V.