The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces
Volume 182 / 2004
Fundamenta Mathematicae 182 (2004), 41-52
MSC: Primary 54F45; Secondary 54E15, 54E35, 54E52.
DOI: 10.4064/fm182-1-2
Abstract
We prove that every Baire subspace $Y$ of $c_0(\mit\Gamma)$ has a dense $G_\delta$ metrizable subspace $X$ with $\dim X \leq \dim Y$. We also prove that the Kimura–Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.
