A continuum is a metric compact connected space. A continuum is chainable if it is an inverse limit of arcs. A continuum is weakly chainable if it is a continuous image of a chainable continuum. A space X is uniquely arcwise connected if any two points in X are the endpoints of a unique arc in X. D. P. Bellamy asked whether if X is a weakly chainable uniquely arcwise connected continuum then every mapping f: X → X has a fixed point. We give a counterexample.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-6,
author = {Miros\l aw Sobolewski},
title = {A weakly chainable uniquely arcwise connected continuum without the fixed point property},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {81-86},
zbl = {1314.54021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-6}
}
Mirosław Sobolewski. A weakly chainable uniquely arcwise connected continuum without the fixed point property. Fundamenta Mathematicae, Tome 228 (2015) pp. 81-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-6/