Strong digital topological complexity of digital maps

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-04-29 DOI:10.1016/j.topol.2024.108934

Zhiguo Zhang , Jingyan Li , Jie Wu

引用次数: 0

Abstract

In the paper, we study a digital topological complexity of a digital map and its properties. Firstly, we discuss a strong digital homotopy which allows iterative algorithms based on our previous work. As a generalization of the topological complexity in terms of the strong digital homotopy (we call it strong digital topological complexity), we next study the strong digital f-sectional category of a strong digital fibration. Then we investigate estimates of the upper and lower bounds for the strong digital topological complexity of digital maps. We also reveal the difference between the strong digital topological complexity and the ordinary digital ones. It has shown that the strong digital topological complexity is more similar to the classical continuous case than the ordinary digital ones. Moreover, arising from practical considerations in robotics, we consider the naive digital topological complexity of digital maps.

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数字地图的强数字拓扑复杂性

本文研究了数字地图的数字拓扑复杂性及其特性。首先，我们讨论了强数字同构，它允许在我们之前工作的基础上进行迭代算法。作为强数字同构拓扑复杂性的广义化（我们称之为强数字拓扑复杂性），我们接下来研究了强数字纤度的强数字节范畴。然后，我们研究了数字映射的强数字拓扑复杂性的上界和下界的估计值。我们还揭示了强数字拓扑复杂性与普通数字拓扑复杂性的区别。结果表明，强数字拓扑复杂性比普通数字拓扑复杂性更类似于经典连续情况。此外，出于机器人技术的实际考虑，我们还考虑了数字地图的天真数字拓扑复杂性。

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.