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Results tagged with topological-groups
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user 3545
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
Accepted
Smoothness as a topological property
The question is a bit awkward, as Pete suggests. First, no need to take an $\ell$-group; an $\ell$-space is the right way to start. Second, you've stated the definition of the word "smooth" in this co …
- 13.3k
6
votes
Is the ability to define Haar measure the main (or only) reason to consider locally compact ...
I can think of two ways to answer this question.
First, regarding your comment "I haven't seen locally compact topological groups used for anything except Fourier analysis," I think the appropriate a …
- 13.3k
8
votes
What is a good book on topological groups?
How about Weil's classic: "L'intégration dans les groupes topologiques et ses applications"? You won't find Kazhdan's Property T nor Tannaka reconstruction, but it treats the other topics deeply and …