Mean dimension of full shifts

Abstract

Let $K$ be a finite dimensional compact metric space and $K^{\mathbb{Z}}$ the full shift on the alphabet $K$. We prove that its mean dimension is given by $\dim K$ or $\dim K-1$ depending on the "type" of $K$. We propose a problem which seems interesting from the view point of infinite dimensional topology.

arXiv comment9 pages

References in corpus (3)

• Cohomological dimension theory of compact metric spaces
• Embedding minimal dynamical systems into Hilbert cubes
• Expansive multiparameter actions and mean dimension