Topological space

A topological space is an abstract mathematical space constituted by any collection of points (an arbitrary set of elements), in which a relation of neighbourhood of one point to a set of points is defined and, consequently, a relation of neighbourhood or adherence of two sets (figures) to one another. This is a generalization of the intuitive intelligible relation of neighbourhood or adherence of figures in ordinary space. Neighbourhood forms a distinctive appurtenance of bodies and gives them the same geometric relation when we retain in them this property and do not take into consideration all others, whether they be essential or accidental. Topology (described separately) provides a rigorous basis for the strict application of arguments relating to the intuitive concept of connectedness in its most general sense.