# Tagged Questions

72 views

### Is there a gap in Serre's proof of inverse function theorem?

On page 73 of 'Lie algebras and Lie groups', Serre proves the inverse function theorem for complete fields. I would like to have some clarification about the following point. Let $K$ be a complete ...
174 views

### equation involving the integral of the modular function of a topological group

Let $G$ be a locally compact topological group and $H$ a closed subgroup. Choose a left Haar measure $d\zeta$ for $H$, and let $d\mu$ be any measure for $G$. Also let $f$ and $g$ be continuous ...
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### What is a one-parameter global Lie group of smooth diffeomorphisms?

consider the one-parameter map acting on $\mathbb{R}^2 (t\in\mathbb{R})$: $f:(t,(x_1,x_2))\mapsto \left( x_1+t, \frac{x_1 x_2}{x_1+t} \right)$. I need to prove, that the function $f$ defines a ...
173 views

### Cauchy's functional equation - a generalisation? (do additive maps have to be continuous?)

If a map $f : \mathbb{R} \to \mathbb{R}$ is additive, in the sense that $f(x + y) = f(x) + f(y)$, then it is simple to show that $f$ is $\mathbb{Q}$-linear, buy it does not need to be ...