Rare Continuity Revisited via δb-open Sets

In this paper we introduce and study the concept of rare δb-continuity in topological spaces as a generalization of rare continuity and weak δb-continuity. We investigate several properties of rarely δb-continuous functions. Rare δb-continuity implied by rare δ-continuity and implies rare b-continuity. We also introduce the concept of I.δb-continuity, which is weaker than δb-continuity and stronger than rare δb-continuity.