Combinatorially rich sets in partial semigroups

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-30 DOI:10.1016/j.topol.2025.109406

Arpita Ghosh , Neil Hindman

引用次数: 0

Abstract

There are several notions of size for semigroups that have natural analogues for partial semigroups. Among these are thick, syndetic, central, piecewise syndetic, IP, J, and the more recently introduced notion of combinatorially rich, abbreviated CR. We investigate the notion of CR set for adequate partial semigroups, its relation to other notions, especially J sets, and some surprising differences among them.

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偏半群中的组合富集

半群的大小有几个概念，它们与部分半群有天然的相似之处。其中包括厚的、综合的、中心的、分段综合的、IP的、J的，以及最近引入的组合丰富的、缩写的CR的概念。我们研究了适当的部分半群的CR集的概念，它与其他概念的关系，特别是J集，以及它们之间的一些惊人的区别。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.