  We investigate one-point reduction methods of finite topological spaces.
These methods allow one to study homotopy theory of cell complexes by means of
elementary moves of their finite models. We also introduce the notion of
h-regular CW-complex, generalizing the concept of regular CW-complex, and prove
that the h-regular CW-complexes, which are a sort of
combinatorial-up-to-homotopy objects, are modeled (up to homotopy) by their
associated finite spaces. This is accomplished by generalizing a classical
result of McCord on simplicial complexes.
