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