SEPARATION AXIOM
Separation axiom 22 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia For the axiom of set theory, see Axiom schema of separation . Separation axioms in topological spaces Kolmogorov classification T 0 (Kolmogorov) T 1 (Fréchet) T 2 (Hausdorff) T 2 ½ (Urysohn) completely T 2 (completely Hausdorff) T 3 (regular Hausdorff) T 3½ (Tychonoff) T 4 (normal Hausdorff) T 5 (completely normal Hausdorff) T 6 (perfectly normal Hausdorff) History An illustration of some of the separation axioms. Grey amorphous broken-outline regions indicate open sets surrounding disjoint closed sets or points: red solid-outline circles denote closed sets while black dots represent points. In topology and related fields of mathematics , there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these rest...