Displaying similar documents to “Continua with unique symmetric product”

A note on the paper ``Smoothness and the property of Kelley''

Gerardo Acosta, Álgebra Aguilar-Martínez (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a continuum. In Proposition 31 of J.J. Charatonik and W.J. Charatonik, , Comment. Math. Univ. Carolin. (2000), no. 1, 123–132, it is claimed that L ( X ) = ⋂ p ∈ X S ( p ) , where L ( X ) is the set of points at which X is locally connected and, for p ∈ X , a ∈ S ( p ) if and only if X is smooth at p with respect to a . In this paper we show that such equality is incorrect and that the correct equality is P ( X ) = ⋂ p ∈ X S ( p ) , where P ( X ) is the set of points at which X is connected im kleinen. We also use the correct equality to obtain some...

On the set function ℘

Sergio Macías (2024)

Commentationes Mathematicae Universitatis Carolinae

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Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, ℘ , and present properties of it.

Monotone retractions and depth of continua

Janusz Jerzy Charatonik, Panayotis Spyrou (1994)

Archivum Mathematicum

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It is shown that for every two countable ordinals α and β with α > β there exist λ -dendroids X and Y whose depths are α and β respectively, and a monotone retraction from X onto Y . Moreover, the continua X and Y can be either both arclike or both fans.

Homeomorphisms of composants of Knaster continua

Sonja Štimac (2002)

Fundamenta Mathematicae

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The Knaster continuum K p is defined as the inverse limit of the pth degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer p ≥ 2, all composants of K p having no endpoints are homeomorphic. This generalizes Bandt’s result which concerns the case p = 2.