The pseudometric topology induced by upper asymptotic density

2024/10/09 by Keith, Jonathan M.
#11B05 #54E50 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2410.06559

Abstract

Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which P(ℕ) is complete. The collection D of sets with asymptotic density is closed in this pseudometric, and closed subsets of D are characterised by a generalisation of an additivity property (AP0).

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