## 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
Full Text: