Semigroup compactifications of automorphism groups of ultrahomogeneous cyclically ordered sets

G. B. Sorin

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: For the automorphism group of an ultrahomogeneous cyclically ordered set (with permutation topology) we describe three proper Ellis semigroup compactifications and compare them with Roelcke-compactification. We show that the group $G$ of transformations of a discrete space (with permutation topology) has a semitopological semigroup compactification and present an initial description of Roelcke-uniformity on $G$.

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

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

Received: 13.01.2025 and 07.07.2025

DOI: 10.4213/sm10259