A fixed point conjecture for Borsuk continuous set-valued mappings

• Autorzy: Dariusz Miklaszewski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 55R25: Sphere bundles and vector bundles
• 57R20: Characteristic classes and numbers
• 54C60: Set-valued maps

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 175
• Numer: 1
• Strony: 69-78

Daty

wydano

2002

Twórcy

autor

Dariusz Miklaszewski

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

Identyfikatory

DOI

10.4064/fm175-1-4