Publication: Universal and proximately universal limits
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Publication Date
1996-08
Authors
Cerin, Z.
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Australian Mathematical Society
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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.
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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.