Geodesic
A weakly chainable uniquely arcwise connected continuum without the fixed point property
Mirosław Sobolewski1
1 Department of Mathematics, Informatics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
Fundamenta Mathematicae, Tome 228 (2015) no. 1, pp. 81-86

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm228-1-6
Keywords: continuum metric compact connected space continuum chainable an inverse limit arcs continuum weakly chainable continuous image chainable continuum space uniquely arcwise connected points endpoints unique arc nbsp nbsp bellamy asked whether weakly chainable uniquely arcwise connected continuum every mapping has fixed point counterexample

Mirosław Sobolewski 1

1 Department of Mathematics, Informatics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Mirosław Sobolewski. A weakly chainable uniquely arcwise connected continuum without the fixed point property. Fundamenta Mathematicae, Tome 228 (2015) no. 1, pp. 81-86. doi: 10.4064/fm228-1-6

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