Metric Mean Dimension and Mean Hausdorff Dimension Varying the Metric

Let f : M → M be a continuous map on a compact metric space M equipped with a fixed metric d, and let τ be the topology on M induced by d. We denote by M(τ) the set consisting of all metrics on M that are equivalent to d. Let mdimM(M,d,f) and mdimH(M,d,f ) be, respectively, the metric mean dimension...