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The definitions provided by the authors of the current study are offered together with a discussion of the recent advances that they have contributed. We begin with an introduction of the concepts of closed and open sets. We explore characteristics and provide an idea of obtained results by adding the notion of FNbϱNOS and analyzing a few of their properties in 𝑓𝑛𝑡𝑠. We've researched the contrasts between the derived, exterior, and frontier notions that are provided.