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- W2074274725 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H upper N> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>HN</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
- W2074274725 created "2016-06-24" @default.
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- W2074274725 date "1992-01-01" @default.
- W2074274725 modified "2023-09-27" @default.
- W2074274725 title "An intrinsic description of shape" @default.
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- W2074274725 doi "https://doi.org/10.1090/s0002-9947-1992-1028311-x" @default.
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