Displaying similar documents to “Ultrasmoothness in dendroids”

Hyperspace retractions for curves

Charatonik Janusz J., Charatonik Włodzimierz J., Omiljanowski Krzysztof, Prajs Janusz R.

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AbstractWe study retractions from the hyperspace of all nonempty closed subsets of a given continuum onto the continuum (which is naturally embedded in the hyperspace). Some necessary and some sufficient conditions for the existence of such a retraction are found if the continuum is a curve. It is shown that the existence of such a retraction for a curve implies that the curve is a uniformly arcwise connected dendroid, and that a universal smooth dendroid admits such a retraction. The...

On smooth dendroids

Janusz Charatonik, Carl Eberhart (1970)

Fundamenta Mathematicae

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Depth of dendroids.

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

Mathematica Pannonica

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Induced open projections and C*-smoothness

Włodzimierz J. Charatonik, Alejandro Illanes, Verónica Martínez-de-la-Vega (2013)

Colloquium Mathematicae

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We show that there exists a C*-smooth continuum X such that for every continuum Y the induced map C(f) is not open, where f: X × Y → X is the projection. This answers a question of Charatonik (2000).