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A Szpilrajn--Marczewski Type Theorem for Concentration Dimension on Polish Spaces

Published:2006-06-01
Printed: Jun 2006
• Józef Myjak
• Tomasz Szarek
• Maciej Ślȩczka
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Abstract

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