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A Szpilrajn–Marczewski Type Theorem for Concentration Dimension on Polish Space
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- Journal:
- Canadian Mathematical Bulletin / Volume 49 / Issue 2 / 01 June 2006
- Published online by Cambridge University Press:
- 20 November 2018, pp. 247-255
- Print publication:
- 01 June 2006
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- Article
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Let
$X$ be a Polish space. We will prove that
$${{\dim}_{T}}X=\inf \left\{ {{\dim}_{L}}{X}'\,:\,{X}'\,\text{is homeomorphic to }X\, \right\},$$where
${{\dim}_{L}}\,X$ and 
${{\dim}_{T}}\,X$ stand for the concentration dimension and the topological dimension of 
$X$, respectively.
