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Questions about the branch of algebra that deals with groups.

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 …
Georges Elencwajg's user avatar
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 …
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 ( …
Georges Elencwajg's user avatar