Upper quasi continuous maps and quasi continuous selections

The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form (G \ I) ∪ J, where G is open and I, J are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form (G \ I) ∪ J.