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Homotopies of bounded width are almost Lipschitz |
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| Authors: | Allan Calder Jerrold Siegel |
| Institution: | Department of Mathematics, New Mexico State University, Las Cruces, NM 88003, USA;Department of Mathematics, Birkbeck College, London WC1, UK;Department of Mathematics, University of Missouri-St. Louis, St. Louis, MO 63121, USA |
| Abstract: | Let Y be a compact Riemannian manifold. Let X be locally compact and paracompact. It is shown that every uniform homotopy and every homotopy of bounded width from X to Y may be approximated by a Lipschitz homotopy. Applications to the study of uniform homotopy and homotopies of bounded width are given. |
| Keywords: | 55Q05 53C20 53C20 path length uniform homotopy Riemanian manifold Lipschitz |
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