On digital H-spaces

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-05-19 DOI:10.1016/j.topol.2025.109426

Wayne A. Johnson , Dae-Woong Lee , P. Christopher Staecker

引用次数: 0

Abstract

We investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between

{NP}_{1}

and

{NP}_{2}

product adjacencies. We explore algebraic properties of digital H-spaces preserved under digital homotopy equivalence, and we give a general construction that produces examples of digital H-spaces that are not homotopy-equivalent to digital topological groups in both categories. Further, we show that this construction essentially classifies all

{NP}_{2}

-digital H-spaces. In a short appendix, we resolve a question that was left unresolved in [16], and complete the full classification of digital topological groups.

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关于数字h空间

研究了数字拓扑图论模型中数字h空间的性质。与之前的工作一样，得到的结果通常从根本上取决于NP1和NP2乘积邻接关系之间的选择。我们探讨了在数字同伦等价下保持的数字h空间的代数性质，并给出了在这两个范畴中与数字拓扑群不同伦等价的数字h空间的一个一般构造。进一步，我们证明了这种构造本质上对所有np2 -数字h空间进行了分类。在一个简短的附录中，我们解决了[16]中未解决的问题，并完成了数字拓扑群的完整分类。

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.