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We investigate further properties of semi-I-open sets and semi-I-continuous functions introduced in [4] and give the notions of semi-I-open and semi-I-closed functions.

We introduce the notions of δ-t-sets, δ β -t-sets, δ-B-continuity and δ β -B-continuity and obtain decompositions of continuity and complete continuity.

Abstract. In this paper, we define and study the concept of Λ s δ -closure operator and the associated topology τ Λ s δ on a topological space (X, τ ) in terms of g.Λ s δ -sets.