Fibrations between finite topological spaces

2019/07/09 by Cianci, Nicolás, Ottina, Miguel · 1 citation
#54C15 (Secondary) #55R05 #55R15 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.03972

Abstract

We study Hurewicz fibrations between finite T₀--spaces from a combinatorial viewpoint and give strong conditions that a continuous map between finite T₀--spaces must satisfy in order to be a Hurewicz fibration. We also show that there exists a strong relationship between Hurewicz fibrations between finite T₀--spaces and Grothendieck bifibrations. Finally we give several interesting examples that illustrate this theory and show that many of the assumptions of our results are necessary.

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