A new class between theta open sets and theta omega open sets

摘要

We define θN-closure operator as a new topological operator which lies between the θ-closure and the θω-closure. Some relationships between this new operator and each of θ-closure, θω-closure, and usual closure are obtained. Via θN-closure operator, we introduce θN-open sets as a new topology. Some mapping theorems related to the new topology are given. T2 topological spaces are characterized in terms of θN-closure operator. Also, we use N-open sets to define N-regularity as a new separation axiom which lies strictly between ω-regularity and regularity. For a given topological space (Y,σ), we show that N-regularity is equivalent to the condition σ=σθN. Finally, θN-continuity, N-θ-continuity, weak θN-continuity, and faint θN-continuity are introduced and studied.