The Separation Axioms (A Topology Visual)

A topology on a set gives a notion of "shape" or "vicinity" (loosely speaking) to the set. There are different classes of topological spaces based on how finely the topology can distinguish between two distinct points or sets in the space.

Here we provide a visual of five levels of this distinguishability: Kolmogorov (T0), Frechet (T1), Hausdorff (T2), Regular Hausdorff (T3), and Normal Hausdorff (T4).

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topology,separation,axioms,hausdorff,topological space,math,mathematics,open set,closed set,point set topology,metric space,