Abstract

In this paper, we introduce and investigate Fermatean Neutrosophic generalized $M$-continuous mappings and Fermatean Neutrosophic generalized $M$-irresolute mappings within the framework of Fermatean Neutrosophic topological spaces. We systematically study the fundamental topological properties of these newly defined classes of mappings, analyze their behavior under set-theoretic operations, and establish their interrelations with other well-known classes in Fermatean Neutrosophic topology. Several illustrative examples are provided to clarify the concepts and demonstrate the applicability of the proposed framework. Additionally, we examine the structural aspects and role of these mappings in preserving Fermatean Neutrosophic generalized $M$-closed sets. The results significantly enrich the theoretical foundation of Fermatean Neutrosophic topology by extending classical ideas of open and closed mappings, and provide potential applications in decision sciences and information systems where uncertainty and vagueness are inherent.

Keywords and Phrases

Fermatean Neutrosophic generalized $M$-closed, Fermatean Neutrosophic generalized $M$-continuous and Fermatean Neutrosophic generalized $M$-irresolute mappings.

A.M.S. subject classification

54A40, 54D30, 03E72.

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