Generalized Quasi-Continuities of Multifunctions on Bitopological Spaces

The aim of the article is to introduce a few variants of generalized quasi-continuity of multifunctions defined on a bitopological space and to study their mutual relationship. The results known for functions are extended to multifunctions which provide a wider range of relationships, mainly in terms of upper and lower semi continuities and corresponding continuities with respect to a dual bitopology. The proof procedures are based on a notion of pseudo refinement of two topologies and the Baire property in a bitopological space. A characterization of some continuities depending on two topologies by continuities depending only on one topology and the structure of the sets of semi discontinuity points are given. The end of the article is dedicated to several interpretations that facilitate and clarify orientation in the achieved results.