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Pathology of submeasures and Fσ ideals

2022/11/03 by Martínez, Jorge, Meza-Alcántara, David, Uzcátegui, Carlos
#FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2211.01544

Abstract

We address some phenomena about the interaction between lower semicontinuous submeasures on ℕ and Fσ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological Fσ ideals. We give a partial answers to the question of whether every nonpathological tall Fσ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological Fσ ideals using sequences in Banach spaces.

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