Szpilrajn type theorem for concentration dimension
Volume 172 / 2002
Fundamenta Mathematicae 172 (2002), 19-25
MSC: Primary 11K55; Secondary 28A78.
DOI: 10.4064/fm172-1-2
Abstract
Let $X$ be a locally compact, separable metric space. We prove that $\dim_{\rm T} X=\inf \{\dim_{\rm L} X': X'\hbox{ is homeomorphic to } X\}$, where $\dim_{\rm L} X$ and $\dim_{\rm T} X$ stand for the concentration dimension and the topological dimension of $X$, respectively.
