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A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces M ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

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 ...

Let T be a tree defined on a metric over a set of paths such that the distance between paths p and q is 1/n, where n is the number of nodes shared by p and q. Let A be a ...

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...

Cohomotopy groups are similar to homotopy groups. A cohomotopy group is a group related to the homotopy classes of maps from a space X into a sphere S^n.

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

On the class of topological spaces, a homeomorphism class is an equivalence class under the relation of being homeomorphic. For example, the open interval (-pi/2,pi/2) and ...