Decompositions of continuity for multifunctions

Investigations of decompositions of continuity for functions between topological spaces has a large literature, but extension of this topic to multifunctions has not yet been investigated. The aim of the present note is to introduce the study of decompositions of continuity for multifunctions. For this purpose we will generalize the methods introduced by the author in [27] and later used in [9] and in many papers including for example [10] and [23].