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# Homology, Homotopy and Applications

## Volume 11 (2009)

### Number 2

### Inverse limits of finite topological spaces

Pages: 223 – 227

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

#### Author

#### Abstract

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.

#### Keywords

finite topological space; simplicial complex; weak homotopy equivalence; inverse limit

#### 2010 Mathematics Subject Classification

55P15, 55U10

Published 1 January 2009