The structure of k_ω spaces and a question of Arhangel'skii's

2020/10/08 by Aldo J. Lazar, Lazar, A. J., D. W. B. Somerset +2
Mathematics · #54B15 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2010.03741

openalex publication_date 2020/10/08 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In 2010 a question of Arhangel'skii's highlighted a gap in the knowledge of k_ω-spaces. His specific question had in fact been answered by Siwiec in 1976, but the highlighted gap still remains. We introduce the simple idea of pure quotient maps, extend Morita's theorem to these, and use Fell's topology to show that every quotient map onto a k_ω-space can be 'purified'; and thus fill the gap, elucidate the structure of k_ω-spaces, and obtain a fuller answer to Arhangel'skii's question.

Related

• Pure quotients and Morita's theorem for k_ω-spaces
• κ-spaces
• ω-Rudin spaces, well-filtered determined spaces and first-countable spaces
• A quotient-like construction involving elementary submodels
• A survey of Kolmogorov quotients