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(external)
Web address : https://doi.org/10.1007/s10958-024-07352-1(external)
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/457891158(external)
Preprint address: https://arxiv.org/abs/2407.00508(external)
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.
Funding information in the publication:
Oleksiy Dovgoshey was supported by grant 359772 of the Academy of Finland.
