Blockers on the pseudo-arc - Illanes, Alejandro (Topology Proceedings, 2021)
Let $X$ be a continuum. Given disjoint nonempty closed subsets $A$ and $B$ of $X, B$ does not block $A$ provided that the union of subcontinua of $X$ intersecting $A$ but not intersecting $B$ is dense in $X$. Answering a question by J. Bobok, P. Pyrih and B. Vejnar in this paper we prove that if $P$ is the pseudo-arc, then there exists a nonempty closed subset $D$ of $P$ such that $D$ blocks each finite set $E$ contained in $P \backslash D$ but there exists a nonempty closed subset $G \subset P \backslash D$ such that $D$ does not block $G$.