About two definitions of F-sensitivity

被引：2

作者：

Kim, Jinhyon ^{[1
]}

Ju, Hyonhui ^{[1
]}

机构：

[1] Kim II Sung Univ, Fac Math, Pyongyang, North Korea

来源：

TOPOLOGY AND ITS APPLICATIONS | 2020年 / 269卷

关键词：

Furstenberg family; F-sensitivity; F-sensitive pair;

D O I：

10.1016/j.topol.2019.106927

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, f) be a topological dynamical system and F be a Furstenberg family. There are two definitions about F-sensitivity of the system (X, f) but unfortunately, by Theorem 6 in Tan and Zhang (2011) [10], these are not equivalent in general. In this paper, we call these two definitions as F-orbit sensitivity and F-diameter sensitivity respectively. And then under the assumption that the dual family kF is countably generated we suggest sufficient and necessary conditions for F-diameter sensitivity and using this result, show that these two definitions are equivalent. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：10

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