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Results tagged with topological-groups
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user 461
A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).
6
votes
Are there locally compact groups which have no compact open subgroups and no discrete infini...
The answer to the title question is No, that is
A locally compact group has a compact open subgroup or a discrete infinite cyclic subgroup.
[Keivan Karai helped me a lot, without being responsible for …
8
votes
4
answers
2k
views
Are there locally compact groups which have no compact open subgroups and no discrete infini...
The posting of this question was suggested by Yemon Choi: see Discrete cyclic subgroup.. The question is not mine; it's just a rephrasing of Discrete cyclic subgroup.
EDIT 4. This post claims that …
1
vote
Discrete cyclic subgroup.
This is a comment. I'm putting it as an answer just to draw attention to the question. (I hope it's ok.) It might be very easy. I'm very curious to know the answer. I'd state the question as follows:
…
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