Notions of separation

Separation axioms refer to the various ways of topologically distinguishing between distinct points (as elements) and disjoint subsets (from an ensemblistic point of view) in a topological space. Many in-betweens are designated by the capital letter T after the initial of the German word "Trennungsaxiom" (Tietze, 1923, Alexandrov and Hopf, 1935) (p. 266 of ), and by numerical indices, in principle all the more restrictive the higher they are and the finer the corresponding topologies (i.e. containing more opens and therefore closes and thus neighborhoods).