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Continuous Functions on the Sphere and Isometries

Published online by Cambridge University Press:  20 November 2018

H. Hadwiger  and
P. Mani
H. Hadwiger
Affiliation:
University of Washington, Seattle
P. Mani
Affiliation:
University of Washington, Seattle
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The theorem of Borsuk-Ulam states that n odd functions on the n-dimensional sphere always have a common zero. We have tried to obtain a similar theorem by "slightly" changing the conditions for the functions, but it turned out that only a very weak analogue can be expected in our case. Here we want to prove a few results and mention some of the questions which have remained unanswered.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 753 - 757
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Binz, J., Stetige Richtungs - und Richtungspaarfunktionale des (n+l)-dimensionalen euklidischen Raumes. (Dissertation, Bern, 1968.)Google Scholar
2. Hadwiger, H., Ungelostes problem Nr. 50. Elemente der Math. 23 (1968) 90.Google Scholar