Algebra · Oct 6, 2026

Radius of comparison equals half the mean dimension

For every minimal homeomorphism h of an infinite compact metrizable space X, the radius of comparison of C(X)⋊hZC(X)\rtimes_h\mathbb Z equals 12mdim(X,h)\tfrac12\mathrm{mdim}(X,h), including infinite values. Zero mean dimension is equivalent to the small boundary property, Jiang–Su stability and finite nuclear dimension; in this case nuclear dimension is at most one.

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