Characterization of ℓ_p-like and c₀-like equivalence relations

2010/06/23 by Longyun Ding, Ding, Longyun
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Rough Sets and Fuzzy Logic #math.GN #math.LO #msc:03E15 #msc:46A46 #msc:54E35

paper · pdf · doi:10.48550/arxiv.1006.4405

8 pages, submitted

arxiv created 2010/06/23 · arxiv updated 2010/06/24

Abstract

Let X be a Polish space, d a pseudo-metric on X. If \(u,v):d(u,v)<δ\ is \bfΠ¹₁ for each δ>0, we show that either (X,d) is separable or there are δ>0 and a perfect set C⊆ X such that d(u,v)≥δ for distinct u,v∈ C. Granting this dichotomy, we characterize the positions of ℓ_p-like and c₀-like equivalence relations in the Borel reducibility hierarchy.

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