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This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-ℐ-set) which is a pragmatic approach to characterize completely  Hausdorff  spaces.

Some strong and weak form of z-continuity via Cl *

Some strong and weak form of z-continuity via Cl ^*