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.
@article{bwmeta1.element.bwnjournal-article-fmv144i3p243bwm,
author = {Wojciech Olszewski},
title = {Universal spaces in the theory of transfinite dimension, I},
journal = {Fundamenta Mathematicae},
volume = {144},
year = {1994},
pages = {243-258},
zbl = {0812.54041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv144i3p243bwm}
}
Olszewski, Wojciech. Universal spaces in the theory of transfinite dimension, I. Fundamenta Mathematicae, Tome 144 (1994) pp. 243-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv144i3p243bwm/
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