On semitopological α-bicyclic monoid

2016/05/30 by Serhii Bardyla, Bardyla, Serhii
Computer Science · Decision Sciences · Mathematics · #20M18 #22A15 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1605.09345

openalex publication_date 2016/05/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a semitopological α-bicyclic monoid B_α and prove that it is algebraically isomorphic to a semigroup of all order isomorphisms between the principal upper sets of the ordinal ω^α. We prove that for every ordinal α for every (a,b)∈ B_α if either a or b is a non-limit ordinal then (a,b) is an isolated point in B_α. We show that for every ordinal α

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