Displaying similar documents to “Hyperspace retractions for curves”

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).

A characterisation of a continuous curve

R. Moore (1925)

Fundamenta Mathematicae

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The purpose of this paper is to prove: Théorème: In order that a continuum M should be a continuous curve it is necessary and sufficient that for every two distinct points A and B of M there should exist a subset of M which consists of a finite number of continua and which separates A from B in M. Théorème: In order that a bounded continuum M should be a continuous curve which contains no domain and does not separate the plane it is necessary and sufficient that for every two distinct...

On smooth dendroids

Janusz Charatonik, Carl Eberhart (1970)

Fundamenta Mathematicae

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Centers of a dendroid

Jo Heath, Van C. Nall (2006)

Fundamenta Mathematicae

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A bottleneck in a dendroid is a continuum that intersects every arc connecting two non-empty open sets. Piotr Minc proved that every dendroid contains a point, which we call a center, contained in arbitrarily small bottlenecks. We study the effect that the set of centers in a dendroid has on its structure. We find that the set of centers is arc connected, that a dendroid with only one center has uncountably many arc components in the complement of the center, and that, in this case,...