Density of the level sets of the metric mean dimension for homeomorphisms

Let N be an n-dimensional compact riemannian manifold, with n ≥ 2. In this paper, we prove that for any α ∈ [0, n], the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to α is dense in Hom(N). More generally, given α, β ∈ [0, n], with α ≤ β, we show the set co...