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Continuous Functions on the Sphere and Isometries
Published online by Cambridge University Press: 20 November 2018
Extract
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.
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- Copyright © Canadian Mathematical Society 1969