Extending a result of McCord, we prove that every finite simplicial complex is homotopy equivalent to the inverse limit of a sequence of finite spaces. In addition to generalizing McCord's theorem, this provides it with a more geometric motivation, demonstrating a sense in which the simplicial complex is successively better approximated by its finite models.
Homology, Homotopy and Applications, Vol. 11 (2009), No. 2, pp.223-227.