Topological and pointwise upper Kuratowski limits of a sequence of lower quasi-continuous multifunctions

Abstract

In this paper we deal with a connection between the upper Kuratowski limit of a sequence of graphs of multifunctions and the upper Kuratowski limit of a sequence of their values. Namely, we will study under which conditions for a graph cluster point (x, y) ϵ X ×ϒ of a sequence {Gr Fn: n ϵ ω} of graphs of lower quasi-continuous multifunctions, y is a vertical cluster point of the sequence {Fn(x): n ϵ ω} of values of given multifunctions. The existence of a selection being quasi-continuous on a dense open set (a dense Gδ-set) for the topological (pointwise) upper Kuratowski limit is established. © 2016, University of Nis. All rights reserved.