Quasi continuous selections of upper Baire continuous mappings

摘要

The paper deals with the existence problem of selections for 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 points of a nowhere dense set. The methods are based on properties of minimal multifunctions and a cluster multi- function generated by a cluster pro cess with respect to the system of all sets of second category with the Baire property.