Let $X$ be a Polish space. We will prove that $$ \dim_T X=\inf \{\dim_L X': X'\text{ is homeomorphic to } X\}, $$ where $\dim_L X$ and $\dim_T X$ stand for the concentration dimension and the topological dimension of $X$, respectively.

Keywords:

Hausdorff dimension, topological dimension, Lévy concentration function, concentration dimension Hausdorff dimension, topological dimension, Lévy concentration function, concentration dimension

MSC Classifications:

11K55, 28A78 show english descriptions Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
Hausdorff and packing measures 11K55 - Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
28A78 - Hausdorff and packing measures

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