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Corpus ID: 237562879

A pasting lemma for Lipschitz functions

@inproceedings{Kvalheim2021APL,
title={A pasting lemma for Lipschitz functions},
author={Matthew D. Kvalheim and Paul Gustafson and Samuel A. Burden},
year={2021}
}

We give a necessary and sufficient condition ensuring that any function which is separately Lipschitz on two fixed compact sets is Lipschitz on their union. The pasting [Mun00, Thm 18.3] (or gluing [Lee11, Lem. 3.23]) lemma asserts that a function which is separately continuous on two closed sets is continuous on their union. To quote [Wea18, p. 7]: “...there is no gluing lemma for Lipschitz functions. A function which is separately Lipschitz on two closed sets, even on two compact sets, need… Expand

Let M (resp. N) be a connected. smooth (= C x ) n-dimensional manifold without boundary. We denote by C x (M) the ring of smooth real valued functions on M and by x(M) the Lie-algebra of all smooth… Expand

Preface.- 1 Introduction.- 2 Topological Spaces.- 3 New Spaces from Old.- 4 Connectedness and Compactness.- 5 Cell Complexes.- 6 Compact Surfaces.- 7 Homotopy and the Fundamental Group.- 8 The… Expand