Ordinal Decompositions and Extreme Selections

Abstract

The paper contains two natural constructions of extreme hyperspace selections generated by special ordinal decompositions of the underlying space. These constructions are very efficient not only in simplifying arguments but also in clarifying the ideas behind several known results. They are also crucial in obtaining some new results for such extreme selections. This is achieved by using special sets called clopen modulo a point. Such sets are naturally generated by a relation between closed sets and points of the space with respect to a given hyperspace selection.