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I Ordered lattice of topologies on the 3 point set

  1. Dec 13, 2017 #1

    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.
  2. jcsd
  3. Dec 17, 2017 #2


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