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A group having continuous group operations. A continuous group is necessarily infinite, since an infinite group just has to contain an infinite number of elements. But some ...

A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

The cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1,...,x_n} are the terms f_1 <= x_1<=g_1 (1) f_2(x_1) <= x_2<=g_2(x_1) (2) | ...

A shift-invariant operator Q for which Qx is a nonzero constant. 1. Qa=0 for every constant a. 2. If p(x) is a polynomial of degree n, Qp(x) is a polynomial of degree n-1. 3. ...

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.

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

A finite-dimensional Lie algebra all of whose elements are ad-nilpotent is itself a nilpotent Lie algebra.

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

The group of rotations and translations.