Genericity of Continuous Maps with Positive Metric Mean Dimension

M. Gromov introduced the mean dimension for a continuous map in late 1990’s, which is an invariant under topological conjugacy. On other hand, notion of metric dynamical system was by Lindenstrauss and Weiss 2000 this refines entropy systems with infinite entropy. In paper we will show if N n dimensional compact riemannian manifold then, any $$a\in [0,n]$$ , set consisting maps equal to dense $$C^{0}(N)$$ $$a=n$$ residual. Furthermore, prove some results related existence and, density maps, defined on Cantor sets, positive also continous product spaces, dimension.