2022-01-23T22:41:56Zhttps://tsukuba.repo.nii.ac.jp/oaioai:tsukuba.repo.nii.ac.jp:000285772021-03-01T14:09:54ZDynamical systems of finite-dimensional metric spaces and zero-dimensional covers加藤, 久男Ikegami, YukiKato, HisaoUeda, AkihideIn this paper, we assume that dimensions mean the large inductive dimension Ind and the covering dimension dim. It is well known that View the MathML source for each metric space X. J. Kulesza (1995) [7] proved the theorem that every compact metric n-dimensional dynamical system with zero-dimensional set of periodic points can be covered by a compact metric zero-dimensional dynamical system via an at most (n+1)n-to-one map. In this paper, we generalize Kuleszaʼs theorem above to the case of arbitrary metric spaces, and improve the theorem. In fact, we prove that every metric n-dimensional dynamical system with zero-dimensional set of periodic points can be covered by a metric zero-dimensional dynamical system via an at most 2n-to-one closed map. Moreover, we also study periodic dynamical systems. We show that each finite-dimensional periodic dynamical system can be covered by a zero-dimensional periodic dynamical system via a finite-to-one closed onto map.journal articleElsevier2013-02application/pdfTopology and its applications3160564574http://hdl.handle.net/2241/1187380166-8641AA00459572https://tsukuba.repo.nii.ac.jp/record/28577/files/TIA_160-3l.pdfeng10.1016/j.topol.2013.01.010© 2013 Elsevier B.V.\nNOTICE: this is the author's version of a work that was accepted for publication in Topology and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Topology and its Applications, Vol.160 Issue3, Pages:564-574. doi:10.1016/j.topol.2013.01.010.