Quasi continuous selections of upper Baire continuous mappings

Abstract

The paper deals with the existence problem of selectionsfor a closed valued and $c$-upper Baire continuous multifunction $F$.The main goal is to find a minimal $usco$ multifunction intersecting $F$and its selection that is quasi continuous everywhere except at pointsof a nowhere dense set. The methods are based on properties of minimalmultifunctions and a cluster multifunction generated by acluster process with respect to the system of all sets of second category with the Baire property.