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 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.
