Mean Topological Dimension for Actions of Discrete Amenable Groups

@inproceedings{Coornaert2005MeanTD,
  title={Mean Topological Dimension for Actions of Discrete Amenable Groups},
  author={Michel Coornaert},
  year={2005}
}
Let G be a countable amenable group containing subgroups of arbitrarily large finite index. Given a polyhedron P and a real number ρ such that 0 ≤ ρ ≤ dim(P ), we construct a closed subshift X ⊂ P having mean topological dimension ρ. This shows in particular that mean topological dimension of compact metrisable G-spaces take all values in [0,∞]. 
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