Geodesic
A fixed point conjecture for Borsuk continuous set-valued mappings
Dariusz Miklaszewski1
1 Faculty of Mathematics and Computer Science Nicholas Copernicus University Chopina 12/18 87-100 Toruń, Poland
Fundamenta Mathematicae, Tome 175 (2002) no. 1, pp. 69-78

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm175-1-4
Keywords: main result paper n every borsuk continuous set valued map closed ball n dimensional euclidean space values which one point sets sets homeomorphic k sphere has fixed point approach fails relevant counterexample homological method fixed point conjecture indicated

Dariusz Miklaszewski 1

1 Faculty of Mathematics and Computer Science Nicholas Copernicus University Chopina 12/18 87-100 Toruń, Poland 
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Dariusz Miklaszewski. A fixed point conjecture for
  Borsuk continuous set-valued mappings. Fundamenta Mathematicae, Tome 175 (2002) no. 1, pp. 69-78. doi: 10.4064/fm175-1-4

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