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

Volume 228 / 2015

Mirosław Sobolewski Fundamenta Mathematicae 228 (2015), 81-86 MSC: Primary 54F15; Secondary 37C25. DOI: 10.4064/fm228-1-6


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.


  • Mirosław SobolewskiDepartment of Mathematics, Informatics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image