A1 Refereed original research article in a scientific journal

On monoids of metric preserving functions




AuthorsBilet, Viktoriia; Dovgoshey, Oleksiy

PublisherFRONTIERS MEDIA SA

Publication year2024

JournalFrontiers in Applied Mathematics and Statistics

Article number1420671

Volume10

eISSN2297-4687

DOIhttps://doi.org/10.3389/fams.2024.1420671(external)

Web address https://doi.org/10.3389/fams.2024.1420671(external)

Self-archived copy’s web addresshttps://research.utu.fi/converis/portal/detail/Publication/457137344(external)


Abstract

Let X be a class of metric spaces and let PX be the set of all f : [0, ∞) → [0, ∞) preserving X, i.e., (Y, f ∘ ρ) ∈ X whenever (Y, ρ) ∈ X. For arbitrary subset A of the set of all metric preserving functions, we show that the equality PX = A has a solution if 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 PX = SI holds.


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Funding information in the publication
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Last updated on 2025-27-01 at 19:44