Contra Functions of Soft Nano Alpha Star Generalized Closed Sets in Soft Nano Topological Spaces

Abstract

Objective: To introduce a new category of contra soft nano functions, labeled as contra soft nano 𝛼∗−generalized continuous and contra soft nano 𝛼∗−generalized irresolute functions in soft nano topological spaces and to identify and analyze their unique properties. This research aims to expand the theoretical framework by exploring these novel functions. Method: The definition of contra soft nano 𝛼∗−generalized continuous and contra soft nano 𝛼∗−generalized irresolute functions is obtained from the previously introduced definition of soft nano 𝛼∗−generalized closed set. The study employs rigorous analysis of these contra soft nano functions and formal proof techniques to establish their properties. Comparative analysis with some existing function classes is conducted to highlight the distinct characteristics of these functions. Findings: The research identifies and confirms the unique features of contra soft nano 𝛼∗−generalized continuous and contra soft nano 𝛼∗−generalized irresolute functions under various operations, supported by detailed proofs and illustrative examples. Novelty: The research contributes to the mathematical literature by defining and exploring a new category of contra soft nano functions and comparing it with some of the existing functions. The counterparts of these properties are validated through illustrations. The formalization of their theoretical framework contributes novel insights and extends the boundaries of soft nano topological spaces.

Keywords: Soft Nano-Open Sets; Soft Nano 𝛼∗ - Generalized Closed Sets; Soft Nano 𝛼∗ - Generalized Open Sets; Contra Soft Nano 𝛼∗ - Generalized Continuous Functions; Contra Soft Nano 𝛼∗ - Generalized Irresolute Functions