Generic homeomorphisms have full metric mean dimension
Abstract
We prove that the upper metric mean dimension of C0-generic homeomorphisms, acting on a compact smooth boundaryless manifold with dimension greater than one, coincides with the dimension of the manifold. In the case of continuous interval maps we also show that each level set for the metric mean dimension is C0-dense in the space of continuous endomorphisms of [0,1] with the uniform topology.
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