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A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

Let M be a sigma-algebra M, and let lambda_1 and lambda_2 be measures on M. If there exists a pair of disjoint sets A and B such that lambda_1 is concentrated on A and ...

Any continuous cumulative frequency curve, such as the one illustrated above in the right figure.

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.

A topological space X is pathwise-connected iff for every two points x,y in X, there is a continuous function f from [0,1] to X such that f(0)=x and f(1)=y. Roughly speaking, ...

The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.

A result in control theory. Define H(psi,x,u)=(psi,f(x,u))=sum_(a=0)^npsi_af^a(x,u). Then in order for a control u(t) and a trajectory x(t) to be optimal, it is necessary ...

The equivalence of manifolds under continuous deformation within the embedding space. Knots of opposite chirality have ambient isotopy, but not regular isotopy.

A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

The sum rule for differentiation states d/(dx)[f(x)+g(x)]=f^'(x)+g^'(x), (1) where d/dx denotes a derivative and f^'(x) and g^'(x) are the derivatives of f(x) and g(x), ...