  It has been argued by Ishikawa and Kato that by making use of a specific
bosonization, $c_M=1$ string theory can be regarded as a constrained
topological sigma model. We generalize their construction for any $(p,q)$
minimal model coupled to two dimensional (2d) gravity and show that the
energy--momentum tensor and the topological charge of a constrained topological
sigma model can be mapped to the energy--momentum tensor and the BRST charge of
$c_M<1$ string theory at zero cosmological constant. We systematically study
the physical state spectrum of this topological sigma model and recover the
spectrum in the absolute cohomology of $c_M<1$ string theory. This procedure
provides us a manifestly topological representation of the continuum Liouville
formulation of $c_M<1$ string theory.
