Blockers in hyperspaces

Given a metric continuum X, let 2 X and C ( X ) denote the hyperspaces of all nonempty closed subsets and subcontinua, respectively. For A , B ∈ 2 X we say that B does not block A if A ∩ B = ∅ and the union of all subcontinua of X intersecting A and contained in X − B is dense in X. In this paper we study some sets of blockers for several kinds of continua. In particular, we determine their Borel classes and, for a large class of locally connected continua X, we recognize them as cap-sets.