In this paper, we assume that dimensions mean the large inductive dimension Ind and the covering dimension dim. It is well known that IndX=dimX 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 Kulesza's 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. © 2013 Elsevier B.V.
CITATION STYLE
Ikegami, Y., Kato, H., & Ueda, A. (2013). Dynamical systems of finite-dimensional metric spaces and zero-dimensional covers. Topology and Its Applications, 160(3), 564–574. https://doi.org/10.1016/j.topol.2013.01.010
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