Non-additivity of the fixed point property for tree-like continua

C. L. Hagopian, and M. M. Marsh. "Non-additivity of the fixed point property for tree-like continua." Fundamenta Mathematicae 231.2 (2015): 113-137. <http://eudml.org/doc/282906>.

@article{C2015,
abstract = {We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point property, but H ∪ K admits a fixed-point-free homeomorphism. In an appendix we verify some of the properties of Bellamy's continuum.},
author = {C. L. Hagopian, M. M. Marsh},
journal = {Fundamenta Mathematicae},
keywords = {continua; tree-like; fixed point property},
language = {eng},
number = {2},
pages = {113-137},
title = {Non-additivity of the fixed point property for tree-like continua},
url = {http://eudml.org/doc/282906},
volume = {231},
year = {2015},
}

TY - JOUR
AU - C. L. Hagopian
AU - M. M. Marsh
TI - Non-additivity of the fixed point property for tree-like continua
JO - Fundamenta Mathematicae
PY - 2015
VL - 231
IS - 2
SP - 113
EP - 137
AB - We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point property, but H ∪ K admits a fixed-point-free homeomorphism. In an appendix we verify some of the properties of Bellamy's continuum.
LA - eng
KW - continua; tree-like; fixed point property
UR - http://eudml.org/doc/282906
ER -