## Algebraic & Geometric Topology

### One-point reductions of finite spaces, $h$–regular CW–complexes and collapsibility

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1763-1780.

Dates
Revised: 5 September 2008
Accepted: 5 September 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796905

Digital Object Identifier
doi:10.2140/agt.2008.8.1763

Mathematical Reviews number (MathSciNet)
MR2448871

Zentralblatt MATH identifier
1227.55005

#### Citation

Barmak, Jonathan; Minian, Elias. One-point reductions of finite spaces, $h$–regular CW–complexes and collapsibility. Algebr. Geom. Topol. 8 (2008), no. 3, 1763--1780. doi:10.2140/agt.2008.8.1763. https://projecteuclid.org/euclid.agt/1513796905

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