The hyperspace of non-blockers of singletons, all the possible examples

2022/12/14 by Alejandro Illanes, Illanes, Alejandro, Benjamín Vejnar +1
Decision Sciences · Mathematics · #54B20 #54F15 #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.2212.07077

openalex publication_date 2022/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a metric continuum X, a nonempty proper closed subspace B of X, does not block a point p∈ X∖ B provided that the union of all subcontinua of X containing p and contained in X∖ B is a dense subset of X. The collection of all nonempty proper closed subspaces B of X such that B does not block any element of X∖ B is denoted by NB(F₁(X)). In this paper we prove that for each completely metrizable and separable space Z, there exists a continuum X such that Z is homeomorphic to NB(F₁(X)). This answers a series of questions by Camargo, Capulín, Castaneda-Alvarado and Maya.

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