Biblioteca de la Universidad Complutense de Madrid

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

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.


URL Oficial:


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.

Tipo de documento:Artículo
Palabras clave:Small multivalued map, multi-net, simple multi-net, approximative map, refinable map, strong shape equivalence, internal movability.
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID: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.

Depositado:07 Nov 2012 10:17
Última Modificación:22 May 2014 09:13

Sólo personal del repositorio: página de control del artículo