Manifolds with corners modeled on convenient vector spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1320.58001
author: Juan Margalef
author: Enrique Outerelo
publication date: 2014-08-12T00:00:00Z
Mathematics Subject Classification ID: 58B10
zbMATH DE Number: 6329475
zbMATH Keywords: quadrants on vector spaces
zbMATH Keywords: bornological space
zbMATH Keywords: Mackey convergence
zbMATH Keywords: Mackey complete spaces
zbMATH Keywords: convenient vector spaces
zbMATH Keywords: differentiation theory in convenient vector spaces
zbMATH Keywords: manifolds with corners
MaRDI profile type: Publication
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title: Manifolds with corners modeled on convenient vector spaces
review text: 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].
reviewed by: Esteban Andruchow
description: scientific article; zbMATH DE number 6329475