A fixed point conjecture for Borsuk continuous set-valued mappings

Volume 175 / 2002

Dariusz Miklaszewski Fundamenta Mathematicae 175 (2002), 69-78 MSC: 54C60, 55M20, 55R25, 57R20. DOI: 10.4064/fm175-1-4


The main result of this paper is that for $n = 3,4,5$ and $k=n-2$, every Borsuk continuous set-valued map of the closed ball in the $n$-dimensional Euclidean space with values which are one-point sets or sets homeomorphic to the $k$-sphere has a fixed point. Our approach fails for $(k,n) = (1,4)$. A relevant counterexample (for the homological method, not for the fixed point conjecture) is indicated.


  • Dariusz MiklaszewskiFaculty of Mathematics and Computer Science
    Nicholas Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland

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