A set together with a collection of subsets, called open sets that satisfy certain axioms. The open sets endow the space with a concept of "nearness" between any two points. This is a generalization of the concept of nearness obtained from a numerical measure of "distance" between two points.
(mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional"
a Cantor space if and only if it is non-empty, perfect, compact, totally disconnected, and metrizable