Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Parametrized Borsuk-Ulam theorems for multivalued maps
HTML articles powered by AMS MathViewer

by Marek Izydorek and Jan Jaworowski PDF
Proc. Amer. Math. Soc. 116 (1992), 273-278 Request permission

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
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
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 273-278
  • MSC: Primary 55M20; Secondary 54C60, 55R25
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1112493-0
  • MathSciNet review: 1112493