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Keywords:
selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity
selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity
Summary:
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 $(G\setminus I)\cup J$, 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 $(G\setminus I)\cup J$.
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