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Given a metric continuum $X$, a nonempty proper closed subspace $B$ of $X$,does not block a point $p\in X\setminus B$ provided that the union of allsubcontinua of $X$ containing $p$ and contained in $X\setminus B$ is a densesubset of $X$. The collection of all nonempty proper closed subspaces $B$ of$X$ such that $B$ does not block any element of $X\setminus B$ is denoted by$NB(F_{1}(X))$. In this paper we prove that for each completely metrizable andseparable space $Z$, there exists a continuum $X$ such that $Z$ is homeomorphicto $NB(F_{1}(X))$. This answers a series of questions by Camargo, Capul\'in,Casta\=neda-Alvarado and Maya.

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