Szpilrajn type theorem for concentration dimension
Szpilrajn type theorem for concentration dimension
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 dimens