Inverse limits of finite topological spaces
Emily Clader · Homology Homotopy and Applications · 2009
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.