Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Parametrized Borsuk-Ulam theorems for multivalued maps


Authors: Marek Izydorek and Jan Jaworowski
Journal: Proc. Amer. Math. Soc. 116 (1992), 273-278
MSC: Primary 55M20; Secondary 54C60, 55R25
MathSciNet review: 1112493
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: By combining parametrized Borsuk-Ulam 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 fixed-point theorems, and they were used by Jaworowski to prove a multivalued version of the Borsuk-Ulam 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55M20, 54C60, 55R25

Retrieve articles in all journals with MSC: 55M20, 54C60, 55R25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1112493-0
PII: S 0002-9939(1992)1112493-0
Article copyright: © Copyright 1992 American Mathematical Society