A New Method to H-Regularize Finite Topological Spaces.

The most useful methods for computing homology of finite topological spaces require that certain regularity conditions are satisfied. In particular, the most suitable algorithmic methods, from the point of view of complexity, are only applicable to h-regular spaces. In this paper, we show a procedure to h-regularize a finite topological space X of height at most 2, that is, to construct an h-regular space that is simple homotopy equivalent to X. This enables us to carry out some topological computations (homology groups) on the h-regular space obtained from this h-regularization process.