On the dichotomy of a locally compact semitopological monoid of order isomorphisms between principal filters of ℕⁿ with adjoined zero

2019/08/22 by Taras Mokrytskyi, Mokrytskyi, Taras
Computer Science · Mathematics · #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1908.08521

openalex publication_date 2019/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n be any positive integer and \mathscrI P F(ℕⁿ) be the semigroup of all order isomorphisms between principal filters of the n-th power of the set of positive integers ℕ with the product order. We prove that a Hausdorff locally compact semitopological semigroup \mathscrI P F(ℕⁿ) with an adjoined zero is either compact or discrete.

Related

• The monoid of order isomorphisms of principal filters of a power of the positive integers
• The monoid of order isomorphisms between principal filters of σℕ^κ
• On compact topologies on the semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set
• Filters and the weakly almost periodic compactification of a\n semitopological semigroup
• Filters and Semigroup Compactification Properties