(Joint work with Sina Greenwood, Robin Knight, Dave MacIntyre, Steve Watson)
T be any map of the set X to itself. A natural question to ask is
whether there is a topology on X with respect to which T is continuous.
Clearly the discrete and indiscrete topologies make any map continuous,
so a better question is `When is there a nice topology on X with
respect to which T is continuous?'
We consider the case when
`nice' is taken to mean compact Hausdorff, and characterize such
functions in terms of their orbit structure. Given the generality of
the problem, the characterization turns out to be surprisingly simple