On monoids of metric preserving functions

2024/04/20 by Viktoriia Bilet, Oleksiy Dovgoshey, Bilet, Viktoriia +1 · 2 citations
Decision Sciences · Mathematics · #20M20 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Fuzzy and Soft Set Theory #General Topology (math.GN) #Primary 26A30 #Secondary 54E35

paper · pdf · doi:10.48550/arxiv.2404.13280

openalex publication_date 2024/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a class of metric spaces and let P_X be the set of all f:[0, ∞)→ [0, ∞) preserving X, (Y, f∘ρ)\inX whenever (Y, ρ)\inX. For arbitrary subset A of the set of all metric preserving functions we show that the equality P_X=A has a solution iff A is a monoid with respect to the operation of function composition. In particular, for the set SI of all amenable subadditive increasing functions there is a class X of metric spaces such that P_X=SI holds, which gives a positive answer to the question of paper [1].

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