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Universal and proximately universal limits

Published online by Cambridge University Press:  09 April 2009

Zvonko Čerin
Affiliation:
Kopernikova 7 10020 Zagreb Croatia e-mail: cerin@cromath.math.hr
Jóse M. R. Sanjurjo
Affiliation:
Departamento de Geometria y Topologia Facultad de Matemáticas Universidad Complutense28040 MadridSpain e-mail: w745@emducm11.bitnet
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Abstract

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We present sufficient conditions on an approximate mapping F: X → Y of approximate inverse systems in order that the limit f: X → Y of F is a universal map in the sense of Holsztyński. 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 Hausdorif space has the proximate fixed point property.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Ho, Chung-wu, ‘On a stability theorem for the fixed-point property’, Fund. Math. 111 (1981), 169177.CrossRefGoogle Scholar
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[3]Holsztyński, W., ‘Universal mappings and fixed point theorems’, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 433438.Google Scholar
[4]Holsztyński, W., ‘A remark on the universal mappings of 1-dimensional continua’, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 547549.Google Scholar
[5]Hu, S. T., Theory of retracts (Wayne State University Press, Detroit, 1965).Google Scholar
[6]Klee, V. L. Jr and Yandl, A., ‘Some proximate concepts in topology’, in: Sympos. Math. 16 (Academic Press, New York, 1974).Google Scholar
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[8]Sanjurjo, José M. R., ‘Stability of the fixed point property and universal maps’, Proc. Amer. Math. Soc. 105 (1989), 221230.CrossRefGoogle Scholar
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