topological spaces

Noun

topological space (plural topological spaces)

1. (formal) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);
   • In order to obtain "intuitive insight" into special classes of topological spaces we can proceed in several ways, only a few of which will be pursued in this chapter. For instance, we can seek to describe important topological spaces by means of enough of their properties to completely characterize...1964, H. J. Kowalsky, translated by Jay E. Strum, Topological Spaces, Academic Press, page 165
2. (broadly, formal) the set X.