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) ? X x Y of a sequence {GrFn:n ? ?} of graphs of lower quasi-continuous multifunctions, y is a vertical cluster point of the sequence {Fn(x): n ? ?} of values of given multifunctions. The existence of a selection being quasi-continuous on a dense open set (a dense G?-set) for the topological (pointwise) upper Kuratowski limit is established.
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