Dendrites with a closed set of end points

Arévalo, Daniel; Charatonik, Włodzimierz J.; Covarrubias, Patricia Pellicer; Simón, Likin

doi:10.1016/s0166-8641(00)00058-4

Cited by 53 publications

(38 citation statements)

References 4 publications

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“…Let X be a dendrite with a countable closure of the set of end points. Then the set O (X) ∩ cl X E( X) is countable and coincides with the set O (X) ∩ (cl X E( X)) (1) . Consider a family {xe x :…”

Section: Lemmamentioning

confidence: 99%

“…A universal element for the family of all dendrites (of order κ, respectively) with a closed set of end points is constructed in [1]. The set of end points of this universal dendrite is homeomorphic to a Cantor ternary set.…”

Section: (13) If a Space E Is Compact And Type(e) = α Then The Ordimentioning

confidence: 99%

“…If X is a dendrite of order κ with a closed set of end points such that (E(X)) (1) = {e X } and e X ∈ E( X), then for any isolated end point p X of X there exists an embedding h : X → Z κ such that h(e X ) = e, h(p X ) = p, and h(E( X)) ⊆ E(Z κ ) (see …”

Section: Basic Constructionsmentioning

confidence: 99%

“…Note that W κ (1) = {e X } and e X ∈ E( X), then the set E( X) is closed and contains exactly one limit end point e X . Thus (P κ 1 )…”

Section: Lemmamentioning

confidence: 99%

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Dendrites with a countable closure of the set of end points

Zafiridou

2008

Topology and its Applications

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Section: Lemmamentioning

confidence: 99%

Section: (13) If a Space E Is Compact And Type(e) = α Then The Ordimentioning

confidence: 99%

Section: Basic Constructionsmentioning

confidence: 99%

“…Note that W κ (1) = {e X } and e X ∈ E( X), then the set E( X) is closed and contains exactly one limit end point e X . Thus (P κ 1 )…”

Section: Lemmamentioning

confidence: 99%

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Dendrites with a countable closure of the set of end points

Zafiridou

2008

Topology and its Applications

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“…Since X ∈ D, X cannot contain neither a topological copy of the dendrite F ω nor a topological copy of the dendrite W (see [7,Theorem 3.3]). Thus, if p ∈ R( X), then for each arc α in X containing p, p is not an acumulation point of R( X) ∩ α and ord p (X) is finite.…”

Section: Lemma 1 Let Y Be a Locally Connected Continuum And Amentioning

confidence: 99%

Dendrites with unique hyperspace C2(X)

Herrera-Carrasco

Illanes

López

et al. 2009

Topology and its Applications

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Let Y be a metric continuum. Let C n (Y ) be the hyperspace of nonempty closed subsets of Y with at most n components. In this paper we show that if X is a dendrite with closed set of end points and C 2 (X) is homeomorphic to C 2 (Y ), for some dendrite Y , then X is homeomorphic to Y . This completes the work by David Herrera-Carrasco and FernandoMacías-Romero who previously proved the corresponding result for each n = 2.

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Minimal sets and orbit spaces for group actions on local dendrites

Marzougui

Naghmouchi

2018

Math. Z.

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We consider a group G acting on a local dendrite X (in particular on a graph). We give a full characterization of minimal sets of G by showing that any minimal set M of G (whenever X is different from a dendrite) is either a finite orbit, or a Cantor set, or a circle. If X is a graph different from a circle, such a minimal M is a finite orbit. These results extend those of the authors for group actions on dendrites. On the other hand, we show that, for any group G acting on a local dendrite X different from a circle, the following properties are equivalent: (1) (G, X) is pointwise almost periodic.(2) The orbit closure relation R = {(x, y) ∈ X × X : y ∈ G(x)} is closed. (3) Every non-endpoint of X is periodic. In addition, if G is countable and X is a local dendrite, then (G, X) is pointwise periodic if and only if the orbit space X/G is Hausdorff.

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Dendrites with a closed set of end points

Cited by 53 publications

References 4 publications

Dendrites with a countable closure of the set of end points

Dendrites with a countable closure of the set of end points

Dendrites with unique hyperspace C2(X)

Minimal sets and orbit spaces for group actions on local dendrites

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