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A map u:R^n->R^n from a domain G is called a map of class C^r if each component of u(x)=(u_1(x_1,...,x_n),...,u_m(x_1,...,x_n)) is of class C^r (0<=r<=infty or r=omega) in G, ...

Given a subset B of a set A, the injection f:B->A defined by f(b)=b for all b in B is called the inclusion map.

A stable fixed point of a map which, in a dissipative dynamical system, is an attractor.

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A map f between topological spaces that maps closed sets to closed sets. If f is bijective, then f is closed <==>f is open <==>f^(-1) is continuous, where f^(-1) denotes the ...

Let a patch be given by the map x:U->R^n, where U is an open subset of R^2, or more generally by x:A->R^n, where A is any subset of R^2. Then x(U) (or more generally, x(A)) ...

An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

In combinatorial logic minimization, a device known as a Karnaugh map is frequently used. It is similar to a truth table, but the various variables are represented along two ...