Delhomme–Laflamme–Pouzet–Sauer space as groupoid

: Dovgoshey, Oleksiy; Kostikov, Alexander

Publisher: Springer

: 2024

: Journal of Mathematical Sciences

: Journal of Mathematical Sciences (United States)

: 284

: 3

: 315

: 328

: 1072-3374

: 1573-8795

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

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

: https://research.utu.fi/converis/portal/detail/Publication/457891158

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

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.

:
Oleksiy Dovgoshey was supported by grant 359772 of the Academy of Finland.