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Results tagged with gr.group-theory
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user 450
Questions about the branch of algebra that deals with groups.
69
votes
Accepted
Is there a compact group of countably infinite cardinality?
No, there is no countably infinite compact Hausdorff topological group.
Indeed such a group $G$ would have a left-invariant Haar measure $m$ with $m(G)=1$
and all points would have the same measure ( …
- 47.5k
7
votes
Two Definitions of "Character" of topological groups
It is easy to miss the point that in the second definition $\mathbb Q/\mathbb Z$ is required to be discrete in Hiro's question.
Hence even if a continuous morphism $f:G\to T$ has image in $\mathbb …
- 47.5k
7
votes
Superfluous definitions
A Lie subgroup of a Lie group is usually defined as a subgroup which is also a submanifold.
But actually any closed subgroup of a Lie group is automatically a manifold, hence a Lie subgroup.
Similarly …