Universal spaces in the theory of transfinite dimension, I
Volume 144 / 1994
Fundamenta Mathematicae 144 (1994), 243-258
DOI: 10.4064/fm-144-3-243-258
Abstract
R. Pol has shown that for every countable ordinal α, there exists a universal space for separable metrizable spaces X with ind X = α . We prove that for every countable limit ordinal λ, there is no universal space for separable metrizable spaces X with Ind X = λ. This implies that there is no universal space for compact metrizable spaces X with Ind X = λ. We also prove that there is no universal space for compact metrizable spaces X with ind X = λ.
