### Impacto

Rodríguez Sanjurjo, José Manuel
(1992)
*An intrinsic description of shape.*
Transactions of the American Mathematical Society, 329
(2).
pp. 625-636.
ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/1992-329-02/S0002-9947-1992-1028311-X/S0002-9947-1992-1028311-X.pdf

## Abstract

We give in this paper a description of the shape category of compacta in terms of multivalued maps. We introduce the notion of a multi-net and prove that the shape category of compacta is isomorphic to the category HN whose objects are metric compacta and whose morphisms are homotopy classes of multi-nets. This description is intrinsic in the sense that it does not make use of external elements such as ANR-expansions or embeddings in appropriate AR-spaces. We present many applications of this new formulation of shape.

Item Type: | Article |
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Uncontrolled Keywords: | Small multivalued map, multi-net, simple multi-net, approximative map, refinable map, strong shape equivalence, internal movability. |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 17048 |

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Deposited On: | 07 Nov 2012 10:17 |

Last Modified: | 22 May 2014 09:13 |

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