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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.

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, a lift is a map h from X to Z such that gh=f. In other words, a lift of f is a map h ...

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

A map projection in which the parallels are represented by concentric circular arcs and the meridians by concurrent curves.

An automorphism which interchanges the two vertices of a regular map at each edge without interchanging the vertices.

The space E of a fiber bundle given by the map f:E->B, where B is the base space of the fiber bundle.

The number obtained by adding the reciprocals of the odd twin primes, B=(1/3+1/5)+(1/5+1/7)+(1/(11)+1/(13))+(1/(17)+1/(19))+.... (1) By Brun's theorem, the series converges ...

Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii r_1 and r_2 whose centers are a ...

Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

If f(x,y) is an analytic function in a neighborhood of the point (x_0,y_0) (i.e., it can be expanded in a series of nonnegative integer powers of (x-x_0) and (y-y_0)), find a ...