The space of Lipschitz maps from a compactum to a locally convex set
type: Item
instance of: scholarly article
title: The space of Lipschitz maps from a compactum to a locally convex set
zbMATH Open document ID: 0675.58013
DOI: 10.1016/0166-8641(89)90030-8
author: K. Sakai
author: Raymond Y. Wong
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: Let X be a non-discrete compact metric space and Y a separable locally compact, locally convex subset of a normed space. It is shown that (C(X,Y),LIP(X,Y)) is an (s,\(\Sigma)\)-manifold pair and that \(LIP_ k(X,Y)\) is a \(\Sigma\)-manifold, where C(X,Y), LIP(X,Y) and \(LIP_ k(X,Y)\) denote respectively the compact-openly topologized space of continuous maps \(X\to Y\) and its subspace of Lipschitz maps and of Lipschitz maps having Lipschitz constant less than k. It is shown that the space of Lipschitz maps of Lipschitz constant at most k need not be a Q-manifold, but conditions are given under which it is.
Mathematics Subject Classification ID: 58D15
Mathematics Subject Classification ID: 57N20
zbMATH DE Number: 4105900
zbMATH Keywords: space of Lipschitz maps
zbMATH Keywords: locally convex set
zbMATH Keywords: (Q,\(\Sigma \) )-manifold pair
zbMATH Keywords: convex set
zbMATH Keywords: (s,\(\Sigma \) )-manifold pair
zbMATH Keywords: \(\Sigma\)-manifolds
reviewed by: David B. Gauld
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90030-8
OpenAlex ID: W2074524872
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description: scientific article; zbMATH DE number 4105900