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SEPARATION AXIOM

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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...