Wiktionary
n. 1 (context topology English) A set, together with a collection of its subsets that form a topology on the set. 2 (context loosely English) The set itself.
WordNet
n. (mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional" [syn: mathematical space]
Wikipedia
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence. Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints. Being so general, topological spaces are a central unifying notion and appear in virtually every branch of modern mathematics. The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.
Usage examples of "topological space".
The trend was at first so minor that we could not be sure it existed, for all social trends are intermixed with other social trends, snarled together like a plate of spaghetti-worse than that, for it takes an abstract topological space of many dimensions (ten or twelve are not uncommon and hardly adequate) to describe mathematically the interplay of social forces.