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The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

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

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

A map T:(M_1,omega_1)->(M_2,omega_2) between the symplectic manifolds (M_1,omega_1) and (M_2,omega_2) which is a diffeomorphism and T^*(omega_2)=omega_1, where T^* is the ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") ...

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

Let a in C and |a|<1, then phi_a(z)=(z-a)/(1-a^_z) is a Möbius transformation, where a^_ is the complex conjugate of a. phi_a is a conformal mapping self-map of the unit disk ...