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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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.
|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
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|Deposited On:||07 Nov 2012 11:17|
|Last Modified:||27 Nov 2012 17:24|
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