Extremally disconnected spaces as u->a,bu->a=bo->c^r_<4)^lr

2021/09/24 by Misha Gavrilovich, Gavrilovich, M.
Mathematics · Medicine · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications

paper · pdf · doi:10.48550/arxiv.2109.12099

openalex publication_date 2021/09/24 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We observe that the notions of a topological space being extremally disconnected, and of a continuous map of compact Hausdorff spaces being proper, and being surjective proper, can each be defined in terms of the Quillen lifting property with respect to a surjective proper morphism of finite topological spaces, i.e. in terms of a monotone map of finite preorders. This reveals the preorders implicit in the statement of the Gleason theorem that extremally disconnected spaces are projective in the category of compact Hausdorff topological spaces, and interprets it as an instance of a weak factorisation system generated by an explicitly given morphism.

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