Set-maximal selections

摘要

The present paper deals with continuous selections f for the Vietoris hyperspace F(X) of all nonempty closed subsets of a space X which are maximal with respect to some closed subset S is contained in X, i.e. with the property that f(T) ∈ S for every I ∈ F(X) with T ∩ S ≠Ø. This gives rise to a common point of view of several extreme-like properties studied before, it also provides an useful tool in classifying disconnectedness-like properties of spaces by continuous selections for the Vietoris hyperspace.