Topology-Semiregular Spaces and Nonhomeomorphic

[topology]

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.

 

[micromass]

Think about finite spaces.