A characterization of piecewise $$\mathscr {F}$$ -syndetic sets

IF 0.7 3区数学 Q2 MATHEMATICS Semigroup Forum Pub Date : 2024-08-28 DOI:10.1007/s00233-024-10468-0

Conner Griffin

引用次数: 0

Abstract

Some filter relative notions of size, $\left( \mathscr {F},\mathscr {G}\right) $-syndeticity and piecewise $\mathscr {F} $-syndeticity, were defined and applied with clarity and focus by Shuungula, Zelenyuk and Zelenyuk (Semigroup Forum 79: 531–539, 2009). These notions are generalizations of the well studied notions of syndeticity and piecewise syndeticity. Since then, there has been an effort to develop the theory around the algebraic structure of the Stone–Čech compactification so that it encompasses these new generalizations. We prove one direction of a characterization of piecewise $\mathscr {F}$-syndetic sets. This completes the characterization, as the other direction was proved by Christopherson and Johnson (Semigroup Forum 104: 28–44, 2021).

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片状 $$mathscr {F}$ -yndetic 集合的特征描述

Shuungula、Zelenyuk 和 Zelenyuk（《半群论坛》第 79 期：531-539，2009 年）清晰地定义并应用了一些关于大小的滤波相对概念：（\left( \mathscr {F},\mathscr {G}\right) \）-协同性（syndeticity）和（\mathscr {F} \）-片断协同性（piecewise \）-协同性（syndeticity）。这些概念是对研究已久的联合性和片断联合性概念的概括。从那时起，人们一直在努力围绕斯通切奇紧凑化的代数结构发展理论，使之包含这些新的概括。我们证明了片向 $\mathscr {F}$-syndetic 集合的一个表征方向。克里斯托弗森和约翰逊证明了另一个方向（《半群论坛》104: 28-44, 2021）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

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