The space of Lipschitz maps from a compactum to a locally convex set
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.
scientific article; zbMATH DE number 4105900