Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces

2013/02/06 by Luca Motto Ros, Philipp Schlicht, Ros, Luca Motto +1
Mathematics · #03E15 #03E60 #54C10 #54E40 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO #msc:03E15 #msc:03E60 #msc:54C10 #msc:54E40

paper · pdf · doi:10.48550/arxiv.1302.1356

37 pages, 2 figures, revised version, accepted for publication in the Festschrift that will be published on the occasion of Victor Selivanov's 60th birthday by Ontos-Verlag. A mistake has been corrected in Section 6

openalex publication_date 2013/02/06 · arxiv created 2013/10/28 · arxiv updated 2013/10/29 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether under suitable set-theoretical assumptions the induced degree-structures are well-behaved.

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