MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Quasi continuous selections of upper Baire continuous mappings
Milan Matejdes

Abstract

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 multifunction generated by a cluster process with respect to the system of all sets of second category with the Baire property.

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Keywords: Quasi-continuity; Baire continuity; usco multifunction; minimal multifunction; selection; cluster point; cluster multifunction.

MSC: 54C60, 54C65, 26E25

Pages:  69--76     

Volume  62 ,  Issue  1 ,  2010