Existence and genericity of finite topological generating sets for homeomorphism groups

Azer Akhmedov, Michael P. Cohen

We show that the topological groups $Dif{f}_{+}^1(I)$ and $Dif{f}_{+}^1({\mathbb{S}}^1)$ of orientation-preserving $C^1$-diffeomorphisms of the interval and the circle, respectively,…