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, LÃ©vy concentration function, concentration dimensionCategories:11K55, 28A78