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- W2020171123 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." @default.
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- W2020171123 date "2005-05-01" @default.
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- W2020171123 title "Absolute extensors and absolute neighborhood extensors in asymptotic categories" @default.
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- W2020171123 doi "https://doi.org/10.1016/j.topol.2004.10.020" @default.
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