Topologically mixing extensions of endomorphisms on Polish groups

IF 0.6 Q3 MATHEMATICS Applied general topology Pub Date : 2022-04-01 DOI:10.4995/agt.2022.15187

John Burke, Leonardo Pinheiro

引用次数: 1

Abstract

In this paper we study the dynamics of continuous endomorphisms on Polish groups. We offer necessary and sufficient conditions for a continuous endomorphism on a Polish group to be weakly mixing. We prove that any continuous endomorphism of an abelian Polish group can be extended in a natural way to a topologically mixing endomorphism on the countable infinite product of said group.

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波兰群上自同态的拓扑混合扩展

本文研究了波兰群上连续自同态的动力学。给出了波兰群上连续自同态弱混合的充分必要条件。证明了任意一个阿贝尔波兰群的连续自同态可以自然地推广到该群的可数无穷积上的拓扑混合自同态。

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.

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