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 $p \in X \backslash B$ provided that the union of all subcontinua of $X$ containing $p$ and contained in $X \backslash B$ 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 $X \backslash B$ is denoted by $N B\left(F_1(X)\right)$. 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 $N B\left(F_1(X)\right)$. This answers a series of questions by Camargo, Capulín, Castan̄eda-Alvarado and Maya.