On the non-existence of certain group topologies
Volume 187 / 2005
Fundamenta Mathematicae 187 (2005), 213-228
MSC: Primary 03E15.
DOI: 10.4064/fm187-3-2
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 $\mathbb R$ cannot be a Polish group either.
