Noun
topological space (plural topological spaces)
(topology, formally) 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);(loosely) the set X.
A 0-dimensional manifold (or differentiable or analytical manifold) is nothing but a discrete topological space. Source: Internet
A continuous map to a topological space X is frequently referred to as a singular n-simplex. Source: Internet
A locally normal space is a topological space where every point has an open neighbourhood that is normal. Source: Internet
Analysis may be distinguished from geometry ; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space ) or specific distances between objects (a metric space ). Source: Internet
A manifold is a topological space that resembles Euclidean space near each point. Source: Internet
A locally regular space is a topological space where every point has an open neighbourhood that is regular. Source: Internet