2025/09/22 by К.Л. Козлов, Kozlov, K. L., B. V. Sorin +1
Computer Science · Decision Sciences · Mathematics · #22A15 #54H15 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2509.17577
openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
Ellis's "functional approach" allows one to obtain proper compactifications of a topological group G if G can be represented as a subgroup of the homeomorphism group of a space X in the topology of pointwise convergence and G-space X is G-Tychonoff. These compactifications, called Ellis compactifications, are right topological monoids and G-compactifications of the group G with its action by multiplication on the left on itself. A comparison is made between Ellis compactifications of G and the Roelcke compactification of G. Uniformity corresponding to the Ellis compactification of G for its representation in a compact space X is established. Proper Ellis semigroup compactifications are described for groups \rm S(X) (the permutation group of a discrete space X) and \rm Aut (X) (automorphism group of an ultrahomogeneous chain X) in the permutation topology and \rm Aut (X) of LOTS X in the topology of pointwise convergence.