On the uniqueness of the n-fold pseudo-hyperspace suspension for locally connected continua

Libreros-López, Antonio; Macías-Romero, Fernando; Herrera-Carrasco, David

doi:10.1016/j.topol.2022.108053

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“…Recently, the study of the (n, m)−fold hyperspace suspension of continua has been addressed in [1], [4], [5], [7]- [9], [13], [14], [16]- [18], [20], [21], [23].…”

Section: Introductionmentioning

confidence: 99%

Properties of the (n, m)−fold hyperspace suspension of continua

Hernández-Valdez¹,

Herrera-Carrasco²,

Macías-Romero³

et al. 2022

Rev Integr temas mat

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Let n, m ∈ N with m ≤ n and X be a metric continuum. We consider the hyperspaces Cn(X) (respectively, Fn(X)) of all nonempty closed subsets of X with at most n components (respectively, n points). The (n, m)−fold hyperspace suspension on X was introduced in 2018 by Anaya, Maya, and Vázquez-Juárez, to be the quotient space Cn(X)/Fm(X) which is obtained from Cn(X) by identifying Fm(X) into a one-point set. In this paper we prove that Cn(X)/Fm(X) contains an n−cell; Cn(X)/Fm(X) has property (b); Cn(X)/Fm(X) is unicoherent; Cn(X)/Fm(X) is colocally connected; Cn(X)/Fm(X) is aposyndetic; and Cn(X)/Fm(X) is finitely aposyndetic.

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“…Recently, the study of the (n, m)−fold hyperspace suspension of continua has been addressed in [1], [4], [5], [7]- [9], [13], [14], [16]- [18], [20], [21], [23].…”

Section: Introductionmentioning

confidence: 99%