کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4659052 | 1344301 | 2013 | 11 صفحه PDF | دانلود رایگان |
In this paper, we assume that dimensions mean the large inductive dimension Ind and the covering dimension dim. It is well known that 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: Topology and its Applications - Volume 160, Issue 3, 15 February 2013, Pages 564-574