准均匀熵与拓扑熵

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-08-28 DOI:10.1016/j.topol.2024.109054

Paulus Haihambo , O. Olela Otafudu

引用次数: 0

摘要

2023 年，Haihambo 和 Olela Otafudu 提出并研究了准度量空间或准均匀空间 X 的均匀连续自映射 ψ 的准均匀熵 hQU(ψ) 概念。本文讨论了拓扑熵函数 h,hf 与准均匀空间 X 上的准均匀熵函数 hQU 之间的联系，其中 h 和 hf 分别是用紧凑集和有限开盖定义的拓扑熵函数。特别是，我们已经证明，对于 T0-准均匀空间 (X,U) 的均匀连续自映射 ψ，当 X 紧凑时，有 h(ψ)≤hQU(ψ) ；如果 X 是紧凑的 T2 空间，则 hQU(ψ)≤hf(ψ) 相等。

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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Quasi-uniform entropy vs topological entropy

In 2023 Haihambo and Olela Otafudu introduced and studied the notion of quasi-uniform entropy $h_{Q U} (ψ)$ for a uniformly continuous self-map ψ of a quasi-metric or a quasi-uniform space X. In this paper, we discuss the connection between the topological entropy functions $h, h_{f}$ and the quasi-uniform entropy function $h_{Q U}$ on a quasi-uniform space X, where h and $h_{f}$ are the topological entropy functions defined using compact sets and finite open covers, respectively. In particular, we have shown that for a uniformly continuous self-map ψ of a $T_{0}$ -quasi-uniform space $(X, U)$ we have $h (ψ) \leq h_{Q U} (ψ)$ when X is compact and $h_{Q U} (ψ) \leq h_{f} (ψ)$ with equality if X is a compact $T_{2}$ space.

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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.