Biblioteca de la Universidad Complutense de Madrid

Universal and proximately universal limits

Impacto

Cerin, Z. y Rodríguez Sanjurjo, José Manuel (1996) Universal and proximately universal limits. Journal of the Australian Mathematical Society , 61 (Part I). pp. 96-105. ISSN 1446-8107

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URL Oficial: http://journals.cambridge.org/abstract_S1446788700000094




Resumen

We present sufficient conditions on an approximate mapping F : H --> Y of approximate inverse systems in order that the limit f : X --> Y of F is a universal map in the sense of Holsztynski. A similar theorem holds for a more restrictive concept of a proximately universal map introduced recently by the second author. We get as corollaries some sufficient conditions on an approximate inverse system implying that the its limit has the (proximate) fixed point property. In particular, every chainable compact Hausdorff space has the proximate fixed point property.


Tipo de documento:Artículo
Palabras clave:inverse system, approximate inverse system, inverse limit, map of inverse systems, map of approximate inverse systems, approximate polyhedron, universal map, proximately universal map, fixed point property, proximate fixed point property
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID:16963
Referencias:

Chung-wu Ho, 'On a stability theorem for the fixed-point property', Fund. Math. I l l (1981), 169-177.

W. Holsztyfiski, 'Une generalisation du th£oreme de Brouwer sur les points invariants', Bull. Acad. Polon. Sci., Ser. sci. math., astronom. etphys. 12 (1964), 603-606.

__ 'Universal mappings and fixed point theorems', Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 15 (1967), 433^38.

__'A remark on the universal mappings of 1-dimensional continua', Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 15 (1967), 547-549.

S. T. Hu, Theory of retracts (Wayne State University Press, Detroit, 1965).

V. L. Klee, Jr. and A. Yandl, 'Some proximate concepts in topology', in: Sympos. Math. 16 (Academic Press, New York, 1974).

S. Mardesic and T. Watanabe, 'Approximate resolutions of spaces and mappings', Glas. Mat. Ser. III 24 (1989), 586-637.

J.M. R. Sanjurjo, 'Stability of the fixed point property and universal maps', Proc. Amer. Math. Soc. 105 (1989), 221-230.

Depositado:31 Oct 2012 11:07
Última Modificación:07 Feb 2014 09:39

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