The hyperspace of non-blockers of singletons, all the possible examples - Illanes, Alejandro; Vejnar, Benjamin (Topology Proceedings, 2023)
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 N B(F_1(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 N B(F_1(X)). This answers a series of questions by Camargo, Capulín, Castan̄eda-Alvarado and Maya.