Inverse limits of finite topological spaces (Q846031)

\textit{M. C. McCord} proved in [Duke Math. J. 33, 465--474 (1966; Zbl 0142.21503)] that every finite simplicial complex is weakly homotopy equivalent to a finite topological space. In this paper, as a generalization, the author proves that any finite simplicial complex is homotopy equivalent to the inverse limit of a sequence of finite spaces by using the barycentric subdivisions of simplicial complexes and the corresponding finite spaces.