Movability and limits of polyhedra
We define a metric d(S), called the shape metric, on the hyperspace 2X of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 1993 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57334 |
| Online Access: | https://hdl.handle.net/20.500.14352/57334 |
| Access Level: | Open access |
| Keyword: | 151.143 515.164.251 515.124 Shape metric Polyhedra Metric space Topología 1210 Topología |
| Summary: | We define a metric d(S), called the shape metric, on the hyperspace 2X of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyhedra in the shape metric. This fact is applied to show that the hyperspace (2R2, d(S)) is separable. On the other hand, we give an example showing that 2R2 is not separable in the fundamental metric introduced by Borsuk. |
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