On compact topologies on the semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set

2024/12/30 by Олег Гутік, Gutik, Oleg, Maksym Shchypel +1
Computer Science · Decision Sciences · Mathematics · #22M15 #54A10 #54D10 #54D30 #54H10 #Advanced Algebra and Logic #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2412.20886

openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study topologization of the semigroup \mathscrO I _n(L) of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set (L,\leqslant). In particular we show that every T₁ left-topological (right-topological) semigroup \mathscrO I _n(L) is a completely Hausdorff, Urysohn, totally separated, scattered space. We prove that on the semigroup \mathscrO I _n(L) admits a unique Hausdorff countably compact (pseudocompact) shift-continuous topology which is compact, and the Bohr compactification of a Hausdorff topological semigroup \mathscrO I _n(L) is the trivial semigroup.

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