#### Volume 8, issue 3 (2008)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
One-point reductions of finite spaces, $h$–regular CW–complexes and collapsibility

### Jonathan Ariel Barmak and Elias Gabriel Minian

Algebraic & Geometric Topology 8 (2008) 1763–1780
##### Abstract

We investigate one-point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of $h$–regular CW–complex, generalizing the concept of regular CW–complex, and prove that the $h$–regular CW–complexes, which are a sort of combinatorial-up-to-homotopy objects, are modeled (up to homotopy) by their associated finite spaces. This is accomplished by generalizing a classical result of McCord on simplicial complexes.

##### Keywords
finite topological spaces, simplicial complexes, regular CW-complexes, collapses, weak homotopy types, posets
##### Mathematical Subject Classification 2000
Primary: 55U05, 55P15, 57Q05, 57Q10
Secondary: 06A06, 52B70