The hyperspaces HS(p,X)

2019/08/16 by Florencio Corona–Vázquez, Corona-Vázquez, Florencio, Russell Aarón Quiñones–Estrella +3
Decision Sciences · Mathematics · #54B05 #54B20 #54F65 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1908.06200

openalex publication_date 2019/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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