All Questions

Consider a compact metric group $G$ [A compact topological group $G$ where the topology is generated by an invariant metric]. I am particularly interested in the case where $G$ is the $n$-dimensional ...

Example 3 at the website tricki proves that every measurable homomorphism of groups from the circle to the non-zero complex numbers is continuous. Is there any analogous (true) statement for ...

Let $T:S^1\to C^\ast$ be a group theoretic homomorphism from the circle to the non-zero complex numbers. Presumably it is true that if $T$ is $L^2$, then it is continuous. Is there a simple proof, or ...

My imperfect understanding is that, by the work of various authors (Gleason, Yamabe, Montgomery, Zippin ...), the following result is known: Let $G$ be a connected, locally compact, Hausdorff group, ...

I am looking for a reference for the assertion in the title. This assertion is proved in a comment of user nfdc23 to this question. Has any proof of this assertion been published?

In flipping through the Springer lecture notes on Serre's 1964 'Lie Algebras and Lie Groups' lectures at Harvard, I found this pair of suprising results (page 157): Let $G$ be a locally compact group....