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

Myjak, Józef; Szarek, Tomasz

Fundam. Math. 172, No. 1, 19-25 (2002).

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.

Reviewer: Sophia L.Kalpazidou (Thessaloniki)

MSC:

37B99	Topological dynamics
54E45	Compact (locally compact) metric spaces
28A78	Hausdorff and packing measures

Keywords:

Hausdorff dimension; topological dimension; Lévy concentration function; concentration dimension; locally compact separable metric space