A combinatorial characterization of Hurewicz cofibrations between finite\n topological spaces

2018/02/27 by Nicolás Cianci, Cianci, Nicolás, Miguel Ottina +1 · 1 citation
Mathematics · Decision Sciences · Computer Science · #Advanced Topology and Set Theory #Fuzzy and Soft Set Theory #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.1802.10006

Abstract

We characterize the Hurewicz cofibrations between finite topological spaces,\nthat is, the continuous functions between finite topological spaces that have\nthe homotopy extension property with respect to all topological spaces. In\nparticular, we show that cofibrations between connected non-empty finite\ntopological spaces are homotopy equivalences. As a consequence of our\ncharacterization, we obtain a simple algorithm capable of determining whether a\ngiven continuous function between finite topological spaces is a cofibration.\n

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