We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ a certain Polishable subgroup of which shares its topological dimension and descriptive complexity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-3-4,
author = {Todor Tsankov},
title = {Compactifications of $\mathbb{N}$ and Polishable subgroups of $S\_{$\infty$}$
},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {269-284},
zbl = {1104.54016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-3-4}
}
Todor Tsankov. Compactifications of ℕ and Polishable subgroups of $S_{∞}$
. Fundamenta Mathematicae, Tome 189 (2006) pp. 269-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-3-4/