A fixed point conjecture for Borsuk continuous set-valued mappings

Dariusz Miklaszewski. "A fixed point conjecture for Borsuk continuous set-valued mappings." Fundamenta Mathematicae 175.1 (2002): 69-78. <http://eudml.org/doc/282641>.

@article{DariuszMiklaszewski2002,
abstract = {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.},
author = {Dariusz Miklaszewski},
journal = {Fundamenta Mathematicae},
keywords = {Borsuk continuous; fixed point; set-valued functions},
language = {eng},
number = {1},
pages = {69-78},
title = {A fixed point conjecture for Borsuk continuous set-valued mappings},
url = {http://eudml.org/doc/282641},
volume = {175},
year = {2002},
}

TY - JOUR
AU - Dariusz Miklaszewski
TI - A fixed point conjecture for Borsuk continuous set-valued mappings
JO - Fundamenta Mathematicae
PY - 2002
VL - 175
IS - 1
SP - 69
EP - 78
AB - 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.
LA - eng
KW - Borsuk continuous; fixed point; set-valued functions
UR - http://eudml.org/doc/282641
ER -