A fixed point conjecture for Borsuk continuous set-valued mappings
Tom 175 / 2002
Fundamenta Mathematicae 175 (2002), 69-78
MSC: 54C60, 55M20, 55R25, 57R20.
DOI: 10.4064/fm175-1-4
Streszczenie
The main result of this paper is that for 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.
