Nonblockers in hyperspaces

Using nonblockers in hyperspaces (Illanes and Krupski (2011) [3]), we characterize some classes of locally connected continua: the simple closed curve, the arc, trees, and dendrites. We prove that the simple closed curve is the unique locally connected continuum for which the set of nonblockers of singletons is a continuum. We show that the set of nonblockers is also a continuum for the circle of pseudo-arcs.