ON CERTAIN GENERALIZATION OF SPLIT CONTINUITY AND ITS TOPOLOGICAL CONSEQUENCES

In the context of functions between topological spaces, we introduce a weaker form of split continuity [G. Beer, C. Bloomfield, G. Robinson, Split continuity, J. Math. Anal. Appl., 474 (2019), 833--851], namely finitely split continuity. We examine its association with upper semicontinuous multifunctions from a wider perspective. An interesting aspect of this investigation is the significant involvement of the closure of the function's graph. In the final section, we analyze the concept of finitely split continuity more thoroughly within metric spaces.