Absolute extensors and absolute neighborhood extensors in asymptotic categories |
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Authors: | Marcin Sawicki |
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Institution: | Faculty of Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland |
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Abstract: | This paper deals with extending maps in asymptotic categories, i.e., in categories consisting of metric spaces and asymptotically Lipschitz coarsely proper maps. We demonstrate certain examples of absolute extensors and absolute neighborhood extensors. We give some conditions under which a version of Borsuk's homotopy extension theorem holds in these categories, and in answer to a problem posed by Dranishnikov in Russian Math. Surveys 55 (2000) 1085] we show the failure of a general homotopy extension theorem. Finally, we show that a pair of an Hadamard space and its convex subspace has the homotopy extension property. |
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Keywords: | Coarse geometry Asymptotic category Asymptotically Lipschitz map Extensor Homotopy extension theorem |
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