Mean dimension of full shifts

Masaki Tsukamoto

Published 2017-12-08Version 1

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.