Ordered lattice of topologies on the 3 point set

[jackferry]

So I made this diagram of the order imposed on the set of topologies on a 3 point set. Each small circle is a topology with the circle elements being the open sets. The larger circles join isomorphic topologies together. The ordering was messy when I tried to draw inclusion from each topology to its relations, so I stuck to drawing arrows from an isomorphic collection to the isomorphic collections its elements belonged to. Any advice, criticisms, feedback? Did I do this correctly? Does the premise make sense? I'm just getting into point set topology, so this very well could be misguided.

 

[robphy]

possibly useful: https://www.math.stonybrook.edu/~olga/mat364-fall14/soln-hw4.pdf