The action of the automorphism group $\mathrm{\mathrm{Aut}}(X,R)$ (in the topology of pointwise convergence) on the ultrahomo\-geneous cyclically ordered space $(X,R)$ (in the topology of cyclic order) is considered. It is shown that for this action there exists a unique equiuniformity on $(X,R)$, a description of the corresponding proper Ellis semigroup compactification of $\mathrm{\mathrm{Aut}}(X,R)$ is given, and a comparison is made of the corresponding Ellis equiuniformity on $\mathrm{\mathrm{Aut}}(X,R)$ with Roelcke-uniformity ($\mathrm{\mathrm{Aut}}(X,R)$ Roelcke-precompact).
Keywords: cyclically ordered set, automorphism, semigroup, uniformity, compactification
Received December 23, 2024
Revised February 20, 2025
Accepted February 24, 2025
Funding Agency: The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no.075-15-2022-284.
Georgii Borisovich Sorin, doctoral student, Lomonosov Moscow State University, Moscow, 119991 Russia; Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia, e-mail: georgsorin@yandex.ru
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Cite this article as: G.B. Sorin. Ellis uniformities on ultratransitive groups of automorphisms of cyclically ordered spaces. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 1, pp. 185–198.
