Tagged Questions
0
votes
0answers
41 views
Is the Hilbert-Smith conjecture still unsolved?
Conjecture Let $G$ be a locally compact topological group. If $G$ has a continuous faithful group action on an $n$-manifold, then
$G$ is a Lie group.
Is this conjecture still unsolved? Is ...
4
votes
1answer
99 views
Why are locally compact groups Weil complete?
Why are locally compact groups Weil complete?
Note: A topological group $G$ is Weil complete if every left Cauchy net in $G$ is convergent.
Thank you, and sorry if I have bad writing.
10
votes
1answer
144 views
subgroup of connected locally compact group
I need a reference or a short proof for the following property:
A nontrivial connected locally compact group $G$ contains an infinite abelian subgroup.
6
votes
1answer
290 views
A net version of dominated convergence?
Let $G$ be a locally compact Hausdorff Abelian topological group. Let $\mu$ be a Haar measure on $G$, i.e. a regular translation invariant measure. Let $f$ be fixed in $\mathcal{L}^1(G, \mu)$. ...
3
votes
1answer
147 views
If both $H$ and $G/H$ are locally compact then $G$ is locally compact (topological Group)
How do I prove this statement?
Let $G$ be a Topological group and let $H$ be a subgroup of $G$, if both $H$ and $G/H$ are locally compact then $G$ is locally compact. (we will endow the set $G/H$ ...
3
votes
1answer
104 views
$\sigma$- compact clopen subgroup.
I am given $G$ locally compact group, and I want to show that there exists a clopen subgroup $H$ of $G$ that is $\sigma$-compact.
So here's what I did so far:
for $e \in U$, where $U$ is a nbhd of ...
0
votes
1answer
201 views
Transitive group actions and homogeneous spaces
Given a topological group $G$ and a space $X$ with a transitive $G$ action, let $G_x$ be the isotropy group of a point. In Folland "A course in harmonic analysis", there is a statement that $X$ is ...
4
votes
1answer
101 views
Is there any relation between a group being unimodular and having equivalent uniform structures?
Recall: A topological group is said to have equivalent uniform structures if its left and right uniform structures coincide. A locally compact group is said to be unimodular if left Haar measures and ...
2
votes
1answer
171 views
Compact group actions and automatic properness
I am currently re-reading a course on basic algebraic topology, and I am focussing
on the parts that I feel I had very little understanding of. There is one exercise
in the chapter devoted to groups ...
