1
vote
0answers
37 views

Is every regular paratopological group completely regular?

This problem is presented as an open problem 1.31. on p.26 of Arhangel'skii-Tkachenko, Topological groups and related structures. Is this problem still open? Dusan
4
votes
2answers
106 views

A theorem of Markov about completely regular spaces and topological groups

In Pontriaguin's classic book Grupos continuos (in English Continuous Groups), says that A. Markov proved that: There are topological groups that are not normal. Furthermore, he says it is ...
7
votes
2answers
389 views

Conditions for a topological group to be a Lie group

In flipping through the Springer lecture notes on Serre's 1964 'Lie Algebras and Lie Groups' lectures at Harvard, I found this pair of suprising results (page 157): Let $G$ be a locally compact ...
1
vote
1answer
217 views

Recommend a book about compact subgroups

Hi, could you please recommend me some books/articles where I could find information about compact subgroups of metric topological compact (abelian) groups? Thanks in advance for any help.
4
votes
0answers
85 views

A dynamical property of automorphisms of a locally compact group

Let $G$ be a Hausdorff locally compact group and let $\alpha$ be an automorphism of $G$. Say $\alpha$ is (forwards) topologically recurrent if for all $g \in G$ and all neighbourhoods $O$ of $g$, the ...
2
votes
3answers
415 views

When is a topological group Hausdorff (separated)?

Does someone knows a good reference for the following result? "A topological group is Hausdorff if and only if the identity is closed." I have seen proofs in lecture notes of courses on the web, but ...
8
votes
0answers
247 views

'Infinitesimal' elements of a topological group

Let $G$ be a topological group, and let $M$ be the intersection of all conjugacy-invariant neighbourhoods of the identity in $G$ (in other words, the set of elements that can be taken arbitarily close ...
7
votes
4answers
644 views

Measures on general topological groups

I am interested in the group algebras of non-locally compact groups. What references can you advise? This is a wide question, so I list more concretely what I would like to see: Here X can be even ...
3
votes
1answer
240 views

Why does the generic pair generate a dense subgroup of a connected compact Polish group? (cf. Schreier and Ulam)

A result of Schreier and Ulam from their 1935 paper "Sur le nombre des g$\acute{\textrm{e}}$n$\acute{\textrm{e}}$rateurs d'un groupe topologique compact et connexe" says that if $G$ is a connected ...
13
votes
7answers
2k views

Haar measure on a quotient, References for.

I remember reading Weil's "Basic Number Theory" and giving up after a while. Now I find myself thinking of it(thanks to some comments by Ben Linowitz). Right from the very beginning, Weil uses the ...