differentiation theory in convenient vector spaces
Manifolds with corners modeled on convenient vector spaces
Manifolds with corners are infinite dimensional generalizations of finite dimensional manifolds with smooth boundaries. The authors performed a study of manifolds with corners, when the manifolds are modelled in Banach spaces, in a previous work. In the present paper, they extend their interest to manifolds modelled on convenient vector spaces. The necessary differential calculus in this context is developed.NEWLINENEWLINERecall that a convenient vector space \((E,\tau)\) is a Hausdorff locally convex topological vector space in which every Mackey-Cauchy net is convergent. A net \(\{x_\gamma: \gamma\in\Gamma\}\) is a Mackey-Cauchy net in \((E,\tau)\) if there exists a bounded absolutely convex subset \(B\) of \(E\) and a net \(\{\mu_{\gamma,\gamma'}: (\gamma,\gamma')\in\Gamma\times\Gamma\}\) in \(\mathbb{R}\), which converges to zero, such that NEWLINE\[NEWLINE x_\gamma-x_{\gamma'}\in\mu_{\gamma,\gamma'}\cdot B NEWLINE\]NEWLINE for all \((\gamma,\gamma')\in\Gamma\times\Gamma\).NEWLINENEWLINEFor the entire collection see [Zbl 1287.00022].
scientific article; zbMATH DE number 6329475