A weakly chainable uniquely arcwise connected continuum without the fixed point property
Volume 228 / 2015
Fundamenta Mathematicae 228 (2015), 81-86
MSC: Primary 54F15; Secondary 37C25.
DOI: 10.4064/fm228-1-6
Abstract
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 $f:X\to X$ has a fixed point. We give a counterexample.
