- 著者
- Kada Masaru Tomoyasu Kazuo Yoshinobu Yasuo
- 出版者
- Elsevier
- 雑誌
- Topology and its Applications (ISSN:01668641)
- 巻号頁・発行日
- vol.153, no.17, pp.3313-3319, 2006-11
- 被引用文献数
- 1
- 著者
- Ikegami Yuki Kato Hisao Ueda Akihide
- 出版者
- Elsevier
- 雑誌
- Topology and its applications (ISSN:01668641)
- 巻号頁・発行日
- vol.160, no.3, pp.564-574, 2013-02
- 被引用文献数
- 5 5
In 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.