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Displaying similar documents to “A counterexample in non-metric continua theory”

Local connectivity, open homogeneity and hyperspaces.

J. J. Charatonik (1993)

Revista Matemática de la Universidad Complutense de Madrid

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In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua...

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.