A couple days a go, I saw some nice visualisations of separation axioms on Wikipedia. Unfortunately, it wasn’t a full set. Well, here is a full set (well, T0, T1, T2, T2 1/2, T3, T4, T5):
T2 1/2, Completely Hausdorff:
T3 1/2 isn’t in here because of the difficulties in visualising it. The definitions of the separation axioms I used to make these are taken from Counterexamples In Topology.
The following visualizations of T3.5 and T4.5 are based off what I saw in a topology course I’m taking with Dror Bar-Natan. The course is based on Munkres, and the same visualisations may be there.
(the red is the real valued function.)