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For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

A pointed space is a topological space X together with a choice of a basepoint x in X. The notation for a pointed space is (X,x). Maps between two pointed spaces must take ...

A triple (S,S,P) on the domain S, where (S,S) is a measurable space, S are the measurable subsets of S, and P is a measure on S with P(S)=1.

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 ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

Informally, the sample space for a given set of events is the set of all possible values the events may assume. Formally, the set of possible events for a given random ...

Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

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 ...

A fiber space, depending on context, means either a fiber bundle or a fibration.

A topological space in which every point has a countable neighborhood system base for its neighborhood system.