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Topology-Semiregular Spaces and Nonhomeomorphic

  1. Mar 27, 2015 #1
    For a space (X,T) must there be a topology W on X coarser than T such that (X,W) is semiregular other than the indiscrete topology and if so are there two such nonhomeomorphic topologies neither of which are the indiscrete topology?

    I know that any regular space is semi regular and that for instance R and R^2 are nonhomeomorphic.
  2. jcsd
  3. Mar 31, 2015 #2
    Think about finite spaces.
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