Hyperspaces C(p,X) of finite graphs

Corona-Vázquez, Florencio; Quiñones-Estrella, Russell Aarón; Sánchez–Martínez, Javier; Villanueva, Hugo

doi:10.1016/j.topol.2018.08.007

Cited by 3 publications

(4 citation statements)

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“…In [1], it defines in K(X) the following equivalence relation, C(p, X) ∼ C(q, X) if and only if C(p, X) is homeomorphic to C(q, X). Given a positive integer n and a continuum X, it is say that K(X) has size n if the quotient K(X)/ ∼ has cardinality n. In [1], the authors shown that in the class of graphs X, the size of K(X) can be different of the homogeneity degree of X. As a concequence of Theorem 4.14, in the following result, we obtain a partial solution of [1,Problem 5.4,p.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Given a positive integer n and a continuum X, it is say that K(X) has size n if the quotient K(X)/ ∼ has cardinality n. In [1], the authors shown that in the class of graphs X, the size of K(X) can be different of the homogeneity degree of X. As a concequence of Theorem 4.14, in the following result, we obtain a partial solution of [1,Problem 5.4,p. 49].…”

Section: Acknowledgementsmentioning

confidence: 99%

“…The topological structure of the hyperspaces C(p, X) has been recently studied, for example, in [1], [2], [10], [13], [14], and [15], being useful to characterize classes of continua.…”

Section: Introductionmentioning

confidence: 99%

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Uniqueness of the hyperspaces $C(p,X)$ in the class of trees

Corona-Vázquez,

Quiñones-Estrella,

Sánchez-Martínez

et al. 2019

Preprint

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Given a continuum X and p ∈ X, we will consider the hyperspace C(p, X) of all subcontinua of X containing p. Given a family of continua C, a continuum X ∈ C and p ∈ X, we say that (X, p) has unique hyperspace C(p, X) relative to C if for each Y ∈ C and q ∈ Y such that C(p, X) and C(q, Y ) are homeomorphic, then there is an homeomorphism between X and Y sending p to q. In this paper we study some topological and geometric properties about the structure of C(p, X) when X is a tree, being the main result that (X, p) has unique hyperspace C(p, X) relative to the class of trees.

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Section: Acknowledgementsmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

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Uniqueness of the hyperspaces $C(p,X)$ in the class of trees

Corona-Vázquez,

Quiñones-Estrella,

Sánchez-Martínez

et al. 2019

Preprint

Self Cite

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“…The hyperspaces C(p, X) have been very useful to characterize some classes of continua, see for example [31], [32], [33]. In [9] and [10] the authors studied the topological structure of C(p, X) in the case when X is a finite graph.…”

Section: Introductionmentioning

confidence: 99%

The hyperspaces $HS(p,X)$

Corona-Vázquez,

Quiñones-Estrella,

Martínez

2019

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Let X be a continuum and let C(X) denote the hyperspace of subcontinua of X, endowed with the Hausdorff metric. For p ∈ X, define the hyperspace C(p, X) = {A ∈ C(X) : p ∈ A} as a subspace of C(X). In this paper we introduced the quotient space HS(p, X) = C(X)/C(p, X). We present some general properties of HS(p, X) and we study the relationship between the continuum X and the hyperspaces C(X) and HS(p, X).

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