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A topological algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is an algebra and each of the operations f_i^A is continuous in the product topology. Examples of ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

A torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.

Given a complex measure mu, there exists a positive measure denoted |mu| which measures the total variation of mu, also sometimes called simply "total variation." In ...

A "pointwise-bounded" family of continuous linear operators from a Banach space to a normed space is "uniformly bounded." Symbolically, if sup||T_i(x)|| is finite for each x ...

A characterization of normal spaces which states that a topological space X is normal iff, for any two nonempty closed disjoint subsets A, and B of X, there is a continuous ...

The notion of weak amenability was first introduced by Bade et al. (1987), who termed a commutative Banach algebra A "weakly amenable" if every continuous derivation from A ...

The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by <x>=sum_(i=1)^nw_ix_i, (1) where each weight w_i is a nonnegative ...

An expression is called "well-defined" (or "unambiguous") if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be ...

A continuous-time stochastic process W(t) for t>=0 with W(0)=0 and such that the increment W(t)-W(s) is Gaussian with mean 0 and variance t-s for any 0<=s<t, and increments ...