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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An intrinsic description of shape


Author: José M. R. Sanjurjo
Journal: Trans. Amer. Math. Soc. 329 (1992), 625-636
MSC: Primary 54C56; Secondary 54C60, 55P55
MathSciNet review: 1028311
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1028311-X
PII: S 0002-9947(1992)1028311-X
Keywords: Small multivalued map, multi-net, simple multi-net, approximative map, refinable map, strong shape equivalence, internal movability
Article copyright: © Copyright 1992 American Mathematical Society