Displaying similar documents to “Continua with a connected set of points of indecomposability”

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

Mirosław Sobolewski (2015)

Fundamenta Mathematicae

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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.

On partitions in cylinders over continua and a question of Krasinkiewicz

Mirosława Reńska (2011)

Colloquium Mathematicae

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We show that a metrizable continuum X is locally connected if and only if every partition in the cylinder over X between the bottom and the top of the cylinder contains a connected partition between these sets. J. Krasinkiewicz asked whether for every metrizable continuum X there exists a partiton L between the top and the bottom of the cylinder X × I such that L is a hereditarily indecomposable continuum. We answer this question in the negative. We also present a...

Depth of dendroids.

Charatonik, Janusz J., Spyrou, Panayotis (1994)

Mathematica Pannonica

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