A combinatorial characterization of Hurewicz cofibrations between finite topological spaces
Algebraic Topology
2018-02-28 v1 Combinatorics
Abstract
We characterize the Hurewicz cofibrations between finite topological spaces, that is, the continuous functions between finite topological spaces that have the homotopy extension property with respect to all topological spaces. In particular, we show that cofibrations between connected non-empty finite topological spaces are homotopy equivalences. As a consequence of our characterization, we obtain a simple algorithm capable of determining whether a given continuous function between finite topological spaces is a cofibration.
Keywords
Cite
@article{arxiv.1802.10006,
title = {A combinatorial characterization of Hurewicz cofibrations between finite topological spaces},
author = {Nicolás Cianci and Miguel Ottina},
journal= {arXiv preprint arXiv:1802.10006},
year = {2018}
}