Parametrized BorsukUlam theorems for multivalued maps
Authors:
Marek Izydorek and Jan Jaworowski
Journal:
Proc. Amer. Math. Soc. 116 (1992), 273278
MSC:
Primary 55M20; Secondary 54C60, 55R25
MathSciNet review:
1112493
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Abstract: By combining parametrized BorsukUlam theorems proved by Dold with methods using the Vietoris mapping theorem we show that Dold's results can be extended to multivalued maps. Such methods were invented by Eilenberg and Montgomery who applied them to multivalued fixedpoint theorems, and they were used by Jaworowski to prove a multivalued version of the BorsukUlam theorem. Subsequently they were extended and refined in various ways by Górniewicz and others. We also indicate how our results can be proved in the relative case, for pairs of spaces rather than for single spaces only. This allows us to obtain positive results for bundles over manifolds with boundary; for instance, over a closed interval.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199211124930
PII:
S 00029939(1992)11124930
Article copyright:
© Copyright 1992
American Mathematical Society
