Delhomme–Laflamme–Pouzet–Sauer space as groupoid - UTU Research Portal

A1 Refereed original research article in a scientific journal

Delhomme–Laflamme–Pouzet–Sauer space as groupoid

Authors: Dovgoshey, Oleksiy; Kostikov, Alexander

Publisher: Springer

Publication year: 2024

Journal: Journal of Mathematical Sciences

Journal name in source: Journal of Mathematical Sciences (United States)

Volume: 284

Issue: 3

First page : 315

Last page: 328

ISSN: 1072-3374

eISSN: 1573-8795

DOI: https://doi.org/10.1007/s10958-024-07352-1

Web address : https://doi.org/10.1007/s10958-024-07352-1

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457891158

Preprint address: https://arxiv.org/abs/2407.00508

Abstract

Let R+ = [0, ∞) and let d+ be the ultrametric on R+ such that d+(x, y) = max{x, y} for all different x, y ∈ R+. It is shown that the monomorphisms of the groupoid (R+, d+) coincide with the injective ultrametric-preserving functions and that the automorphisms of (R+, d+) coincide with the self-homeomorphisms of R+. The structure of endomorphisms of (R+, d+) is also described.

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AAM_Delhomme–Laflamme–Pouzet–Sauer_2024.pdf

Funding information in the publication:
Oleksiy Dovgoshey was supported by grant 359772 of the Academy of Finland.