The metric mean dimension of hyperspace induced by symbolic dynamical systems. Issue 6 (18th August 2022) - Huang, Xiaojun; Wang, Xian
Abstract : In this paper, we study the relationship of the metric mean dimension between a topological dynamical system ( X, T, d ) and the induced hyperspace topological dynamical system ( 2 X, 2 T, d H ) . Specially, for the topological dynamical system with metric mean dimension is zero, we give three different examples to show that the metric mean dimension of hyperspace dynamical system is zero, finite positive number and infinity, respectively.