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An intrinsic description of shape

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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


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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
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
Deposited On:07 Nov 2012 10:17
Last Modified:12 Dec 2018 15:13

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