Compactifications of ℕ and Polishable subgroups of $S_{\infty }$

Todor Tsankov. "Compactifications of ℕ and Polishable subgroups of $S_{∞}$." Fundamenta Mathematicae 189.3 (2006): 269-284. <http://eudml.org/doc/283280>.

@article{TodorTsankov2006,
abstract = {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 $S_\{∞\}$. As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of $S_\{∞\}$. 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 $S_\{∞\}$ which shares its topological dimension and descriptive complexity.},
author = {Todor Tsankov},
journal = {Fundamenta Mathematicae},
keywords = {compact metrizable space; compactification; descriptive set theory; Polish group; permutation group; topological dimension; almost zero-dimensional space; analytic P-ideal},
language = {eng},
number = {3},
pages = {269-284},
title = {Compactifications of ℕ and Polishable subgroups of $S_\{∞\}$},
url = {http://eudml.org/doc/283280},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Todor Tsankov
TI - Compactifications of ℕ and Polishable subgroups of $S_{∞}$
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 3
SP - 269
EP - 284
AB - 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 $S_{∞}$. As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of $S_{∞}$. 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 $S_{∞}$ which shares its topological dimension and descriptive complexity.
LA - eng
KW - compact metrizable space; compactification; descriptive set theory; Polish group; permutation group; topological dimension; almost zero-dimensional space; analytic P-ideal
UR - http://eudml.org/doc/283280
ER -