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Given a map f from a space X to a space Y and another map g from a space Z to a space Y, does there exist a map h from X to Z such that gh=f? If such a map h exists, then h ...

A map f:R^n|->R which assigns each x a scalar function f(x).

One of the Eilenberg-Steenrod axioms. It states that, for every pair (X,A), there is a natural long exact sequence ...->H_n(A)->H_n(X)->H_n(X,A)->H_(n-1)(A)->..., where the ...

The set of "critical values" of a map u:R^n->R^n of map class C^1 has Lebesgue measure 0 in R^n.

The study of map projections and the making of geographical maps.

A continuous map f:X->Y between topological spaces is said to be null-homotopic if it is homotopic to a constant map. If a space X has the property that id_X, the identity ...

If a map f:G->G^' from a group G to a group G^' satisfies f(ab)=f(b)f(a) for all a,b in G, then f is said to be an antihomomorphism.

A diffeomorphism is a map between manifolds which is differentiable and has a differentiable inverse.

A characteristic of some systems making a transition to chaos. Doubling is followed by quadrupling, etc. An example of a map displaying period doubling is the logistic map.

Given a map f:S->T between sets S and T, the map g:T->S is called a left inverse to f provided that g degreesf=id_S, that is, composing f with g from the left gives the ...