Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

Inverse limits of finite topological spaces

Pages: 223 – 227

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n2.a11


Emily Clader (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)


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

55P15, 55U10

Published 1 January 2009