AUTHOR=Bilet Viktoriia , Dovgoshey Oleksiy 

TITLE=On monoids of metric preserving functions

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1420671

DOI=10.3389/fams.2024.1420671

ISSN=2297-4687

ABSTRACT=<p>Let X be a class of metric spaces and let P<sub>X</sub> be the set of all <italic>f</italic> : [0, ∞) → [0, ∞) preserving X, i.e., (<italic>Y, f</italic> ∘ ρ) ∈ X whenever (<italic>Y</italic>, ρ) ∈ X. For arbitrary subset A of the set of all metric preserving functions, we show that the equality P<sub>X</sub> = 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 P<sub>X</sub> = SI holds.</p><sec><title>2020 Mathematics Subject Classification</title><p>Primary 26A30, Secondary 54E35, 20M20</p></sec>