On the non-existence of certain group topologies

Christian Rosendal. "On the non-existence of certain group topologies." Fundamenta Mathematicae 187.3 (2005): 213-228. <http://eudml.org/doc/283129>.

@article{ChristianRosendal2005,
abstract = {Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.},
author = {Christian Rosendal},
journal = {Fundamenta Mathematicae},
keywords = {group topology; automorphism group; homeomorphism group; category algebra; Borel equivalence relation; descriptive set theory},
language = {eng},
number = {3},
pages = {213-228},
title = {On the non-existence of certain group topologies},
url = {http://eudml.org/doc/283129},
volume = {187},
year = {2005},
}

TY - JOUR
AU - Christian Rosendal
TI - On the non-existence of certain group topologies
JO - Fundamenta Mathematicae
PY - 2005
VL - 187
IS - 3
SP - 213
EP - 228
AB - Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.
LA - eng
KW - group topology; automorphism group; homeomorphism group; category algebra; Borel equivalence relation; descriptive set theory
UR - http://eudml.org/doc/283129
ER -