Nonblockers for hereditarily decomposable continua with the property of Kelley

2022/04/20 by Camargo, Javier, Ferreira, Mayra
#54B20 #54F15 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2204.09645

Abstract

Given a continuum X, let NB (F₁(X)) be the hyperspace of nonblockers of F₁(X). In this paper, we show that if X is hereditarily decomposable with the property of Kelley such that NB (F₁(X)) is a continuum, then X is a simple closed curve. Thus, we characterize the simple closed curve as the unique hereditarily decomposable continuum with the property of Kelley X such that its hyperspace NB (F₁(X)) is a continuum.

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