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Universal and proximately universal limits

Cerin, Z. and 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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Abstract

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.


Item Type:Article
Uncontrolled Keywords: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
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16963
References:

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.

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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.

Deposited On:31 Oct 2012 11:07
Last Modified:07 Feb 2014 09:39

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