由均匀收敛的映射序列生成的非自治系统中的传递性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-04-10 DOI:10.1016/j.topol.2024.108904

Michaela Mlíchová, Vojtěch Pravec

引用次数: 0

摘要

让 (X,d) 是一个度量空间，f1,∞={fn}i=0∞ 是连续映射 fn:X→X 的序列，使得 (fn) 均匀地收敛于一个连续映射 f。我们研究哪些条件可以确保函数 fn 的反演性或非自治系统 (X,f1,∞) 的反演性继承到极限函数 f，反之亦然。例如，A. Fedeli、A. Le Donne 或 J. Li 都曾研究过这个问题，他们给出了从 fn 到 f 继承反演性的不同充分条件。

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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Transitivity in nonautonomous systems generated by a uniformly convergent sequence of maps

Let $(X, d)$ be a metric space and $f_{1, \infty} = {f_{n}}_{i = 0}^{\infty}$ be a sequence of continuous maps $f_{n} : X \to X$ such that $(f_{n})$ converges uniformly to a continuous map f. We investigate which conditions ensure that the transitivity of functions $f_{n}$ or the transitivity of the nonautonomous system $(X, f_{1, \infty})$ is inherited to the limit function f and vice versa. Such problem has been studied for instance by A. Fedeli, A. Le Donne or J. Li who give different sufficient condition for inheriting of transitivity from $f_{n}$ to f. In this paper we give a survey of known result relating to this problem and prove new results concerning transitivity.

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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.