An intrinsic description of shape
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- by José M. R. Sanjurjo PDF
- Trans. Amer. Math. Soc. 329 (1992), 625-636 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 625-636
- MSC: Primary 54C56; Secondary 54C60, 55P55
- DOI: https://doi.org/10.1090/S0002-9947-1992-1028311-X
- MathSciNet review: 1028311