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An intrinsic description of shape


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.

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

S. Bogatyi, Approximate and fundamental retracts, Math. Sb. 22 (1974), 91-103.

K. Borsuk, Theory of retracts, Monogr. Mat. 44, Polish Scientific Publishers, Warszawa, 1967.

_, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223-254.

_, Theory of shape, Monogr. Mat. 59, Polish Scientific Publishers, Warszawa, 1975.

_, Some quantitative properties of shapes, Fund. Math. 93 (1976), 197-212.

J. Dydak, On internally movable compacta, Bull. Acad. Polon. Sei. 27 (1979), 107-110.

J. Dydak and J. Segal, Shape theory: An introduction, Lecture Notes in Math., vol. 688, Springer-Verlag, Berlin, 1978.

_, Strong shape theory, Dissertationes Math. 192 (1981), 1-42.

J. E. Felt, e-continuity and shape, Proc. Amer. Math. Soc. 46 (1974), 426-430.

H. Kato, Refinablem aps in the theory of shape, Fund. Math. 113 (1981), 119-129.

V. L. Klee and A. Yandl, Some proximate concepts in topology, Symposia Math., vol. 16 (INDAM, Rome, 1973), Academic Press, London, 1974, pp. 21-39.

V. F. Laguna and J. M. R. Sanjurjo, Internal fundamental sequences and approximative retracts, Topology Appl. 17 (1984), 189-197.

_, Spaces of approximative maps, Math. Japon. 31 (1986), 623-633.

_, Shape morphisms and spaces of approximative maps, Fund. Math. 183 (1989), 225-235.

S. Mardesic, On Borsuk's shape theory for compact pairs, Bull. Acad. Polon. Sei. 21 (1973), 1131-1136.

S. Mardesic and J. Segal, Shapes of compacta and ANR-systems, Fund. Math. 72 (1971), 41-59.

_, Shape theory, North-Holland, Amsterdam, 1982.

M. A. Moron, On internal movability, internal shape and internal MANR-spaces, Colloq. Math, (to appear).

J. M. R. Sanjurjo, On limits of shape maps, Topology Appl. 23 (1986), 173-181.

_, A non-continuous description of shape, Quart. J. Math. Oxford Ser. 40 (1989), 351-359.

_, Shape morphisms and small multivalued maps, preprint.

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Last Modified:22 May 2014 09:13

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