All Questions
4
questions
12
votes
0
answers
365
views
Does each compact topological group admit a discontinuous homomorphism to a Polish group?
A compact topological group $G$ is called Van der Waerden if each homomorphism $h:G\to K$ to a compact topological group is continuous. By a classical result of Van der Waerden (1933) the groups $SO(...
- 40.2k
9
votes
1
answer
393
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Meager subgroups of compact groups
Suppose we have an infinite compact (Hausdorff) group $G$, and a subgroup $H\leq G$ which is meagre.
Can $H$ always be covered by a countable family of nowhere dense sets $H_n$ such that $H_n^2$ is ...
- 1,132
5
votes
0
answers
212
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On generically Haar-null sets in the real line
First some definitions.
For a Polish space $X$ by $P(X)$ we denote the space of all $\sigma$-additive Borel probability measures on $X$. The space $P(X)$ carries a Polish topology generated by the ...
- 40.2k
4
votes
1
answer
315
views
Is there a topologizable group admitting only Raikov-complete group topologies?
Definition. A group $G$ is called complete (resp. non-topologizable) if each Hausdorff group topology on $G$ is Raikov-complete (resp. discrete). It is clear that each non-topologizable group is ...
- 40.2k