×

Szpilrajn type theorem for concentration dimension. (English) Zbl 0994.37011

Let \(X\) be a locally compact separable metric space. It is proved that \[ \dim_T(X) =\inf\{\dim_LX': X'\text{ is homeomorphic to }X\}, \] where \(\dim_L(X)\) and \(\dim_T(X)\) stand for the concentration dimension and the topological dimension of \(X\), respectively.

MSC:

37B99 Topological dynamics
54E45 Compact (locally compact) metric spaces
28A78 Hausdorff and packing measures
PDF BibTeX XML Cite
Full Text: DOI