All Questions
54 questions
12
votes
1
answer
1k
views
(Closures of sets of) operations in topological groups.
Let $G$ be a topological group. For each $n \in \mathbb{Z}$, consider the continuous functions $f_{n} \colon G \to G : x \mapsto x^{n}$, and set $F := \{f_{n} \mid n \in \mathbb{Z}\}$.
Is there a ...
- 1,498
3
votes
2
answers
483
views
When does a LCA group not contain a (closed) infinite cyclic subgroup?
If $G$ is an LCA (locally compact abelian) group, is there any 'nice' sufficient (or preferably necessary and sufficient) criteria for when $G$ does not contain a closed (and hence discrete in the ...
- 3,115
4
votes
2
answers
2k
views
Irreducible unitary representations of locally compact groups
Let $G$ be a locally compact group and let $\mu$ be a left Haar measure. We know
that $\mu$ is unique up to a scalar in $\mathbf{R}_{>0}$. I don't know so much about unitary representations of ...
- 7,609
9
votes
3
answers
951
views
Is there a non-trivial topological group structure of $\mathbb{Z}$?
More specificaly, is there a haussdorf non-discrete topology on $\mathbb{Z}$ that makes it a topological group with the usual addition operation?
- 1,001