Topological Space

A topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measure by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called topology, which can be defined as a set of neighborhoods for each point that satisfies some axioms formalizing the concept of closeness.
A topological space is the most general type of mathematical space that allows for the definition of limits, continuity, and connectedness. Common types of topological spaces include Euclidian spaces, metric spaces, and manifolds.