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1. CMB 2006 (vol 49 pp. 247)
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A Szpilrajn--Marczewski Type Theorem for Concentration Dimension on Polish Spaces 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 Categories:11K55, 28A78 |