Borsuk's quasi-equivalence is not transitive

Andrzej Kadlof, Nikola Koceić Bilan, and Nikica Uglešić. "Borsuk's quasi-equivalence is not transitive." Fundamenta Mathematicae 197.1 (2007): 215-227. <http://eudml.org/doc/286070>.

@article{AndrzejKadlof2007,
abstract = {Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua X, Y and Z lying in ℝ³ are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.},
author = {Andrzej Kadlof, Nikola Koceić Bilan, Nikica Uglešić},
journal = {Fundamenta Mathematicae},
keywords = {continuum; ANR; inverse sequence; shape; quasi-equivalence; free product of groups; compacta},
language = {eng},
number = {1},
pages = {215-227},
title = {Borsuk's quasi-equivalence is not transitive},
url = {http://eudml.org/doc/286070},
volume = {197},
year = {2007},
}

TY - JOUR
AU - Andrzej Kadlof
AU - Nikola Koceić Bilan
AU - Nikica Uglešić
TI - Borsuk's quasi-equivalence is not transitive
JO - Fundamenta Mathematicae
PY - 2007
VL - 197
IS - 1
SP - 215
EP - 227
AB - Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua X, Y and Z lying in ℝ³ are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.
LA - eng
KW - continuum; ANR; inverse sequence; shape; quasi-equivalence; free product of groups; compacta
UR - http://eudml.org/doc/286070
ER -