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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-2-2,
author = {C. L. Hagopian and M. M. Marsh},
title = {Non-additivity of the fixed point property for tree-like continua},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {113-137},
zbl = {1335.54033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-2-2}
}
C. L. Hagopian; M. M. Marsh. Non-additivity of the fixed point property for tree-like continua. Fundamenta Mathematicae, Tome 228 (2015) pp. 113-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-2-2/