Ellis uniformities on ultratransitive groups of automorphisms of cyclically ordered spaces

G. B. Sorin<sup>ab

a</sup> Lomonosov Moscow State University
^b Moscow Center for Fundamental and Applied Mathematics

Abstract: The action of the automorphism group $\mathrm{Aut}(X,R)$ (in the topology of pointwise convergence) on the ultrahomogeneous 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 $\mathrm{Aut}(X,R)$ is given, and a comparison is made of the corresponding Ellis equiuniformity on $\mathrm{\mathrm{Aut}}(X,R)$ with Roelcke-uniformity ($\mathrm{Aut}(X,R)$ Roelcke-precompact).

Keywords: cyclically ordered set, automorphism, semigroup, uniformity, compactification.

UDC: 512.534.5, 512.536.72, 512.536.75, 515.123.56, 515.126.27

MSC: 22F50, 54H15, 20B27, 20E22, 08A35

Received: 23.12.2024
Revised: 20.02.2025
Accepted: 24.02.2025

DOI: 10.21538/0134-4889-2025-31-1-185-198

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