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The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

The Wolfram Physics Project posits the existence of abstract relations between atoms of space whose pattern defines the structure of physical space. In this approach, two ...

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 ...

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

An orbifold is the object obtained by identifying any two points of a map which are equivalent under some symmetry of the map's group.

A nonsingular linear map A:R^n->R^n is orientation-reversing if det(A)<0.