Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516612 | Topology and its Applications | 2005 | 20 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Marcin Sawicki,