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Theorems of Kakutani and Dyson revisited

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Abstract.

Two theorems of Kakutani and Dyson concerning real-valued functions on a sphere, dating from the middle of the last century, are presented as special cases of a result on stable cohomotopy Euler classes. A complex analogue is also proved and applied to establish a complex version of Dyson’s theorem.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Aberdeen, Aberdeen, AB24 3UE, UK

    M. C. Crabb

  2. Department of Mathematics, Indiana University, Bloomington, IN, 47405-5701, USA

    J. Jaworowski

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  1. M. C. Crabb
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  2. J. Jaworowski
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Correspondence to M. C. Crabb.

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Dedicated to Felix Browder

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Crabb, M.C., Jaworowski, J. Theorems of Kakutani and Dyson revisited. J. fixed point theory appl. 5, 227–236 (2009). https://doi.org/10.1007/s11784-008-0099-9

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  • DOI: https://doi.org/10.1007/s11784-008-0099-9

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