Homology, Homotopy and Applications
Volume 11 (2009)
Inverse limits of finite topological spaces
Pages: 223 – 227
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.
finite topological space; simplicial complex; weak homotopy equivalence; inverse limit
2010 Mathematics Subject Classification