Connected subsets of dendrites and separators of the plane (Q1813284)

The paper consists of four parts. In the first part properties of connected subsets of dendrites are studied. Some characterizations of these spaces are obtained and several necessary and sufficient conditions are found under which such a space is locally compact. The results obtained in the first part are then applied in the second to investigate some special separators of the Euclidean plane. In the third part some families of separators are studied, and in the fourth a full topological description of a special family of separators of the plane is given. This family has appeared in a natural way in investigations of multiselections related to a study of some problems in functional analysis [\textit{B. Ricceri}, Mathematiche 38, 221-235 (1983; Zbl 0625.54025)]. Several questions are asked.