A weakly chainable uniquely arcwise connected continuum without the fixed point property
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.