Non-blockers of decomposable continua with the property of Kelley, and the set function T - Macías, Sergio (Topology Proceedings, 2023)
Given a continuum X, let F_1(X) be the family of singletons of X and let N B(F_1(X)) be the hyperspace of non-blockers of F_1(X). We use Professor Jones’ set function T to present a different proof of the two main theorems of J. Camargo and M. Ferreira in Nonblockers for hereditarily decomposable continua with the property of Kelley. We show a proposition of independent interest, which is key to present a different proof of the second main theorem of Camargo and Ferreira, namely: if X is a hereditarily decomposable continuum with the property of Kelley such that N B(F_1(X)) is a continuum, then X is a simple closed curve. We also prove that if X is a decomposable, not hereditarily decomposable continuum with the property of Kelley and N B(F_1(X)) is a continuum, then the set function T is continuous. Hence, X has a continuous decomposition G such that many elements of G are indecomposable subcontinua of X.