\alpha^{m}}(A)$, $C_{\alpha^{m}}(A)$ and $\alpha^{m}$-open and closed Functions

TL;DR

This paper explores advanced concepts of lpha^{m}-continuity and lpha^{m}-openness in topological spaces, introducing new set functions and examining their properties to deepen understanding of these generalized topological notions.

Contribution

It introduces the functions I_{\u03b1^{m}}(A) and C_{\u03b1^{m}}(A) based on lpha^{m}-open and closed sets, expanding the framework of lpha^{m}-continuity and lpha^{m}-irresoluteness.

Findings

Characterized properties of I_{\u03b1^{m}}(A) and C_{\u03b1^{m}}(A)

Established relationships between lpha^{m}-open/closed maps and these functions

Extended the theory of lpha^{m}-continuity in topological spaces

Abstract

In this paper, we derive more on $\alpha^{m}$-continuous functions and $\alpha^{m}$-irresolute functions with $\alpha^{m}$-open maps and $\alpha^{m}$-closed maps in topological spaces also we introduce $I_{\alpha^{m}}(A)$ and $C_{\alpha^{m}}(A)$ by using the $\alpha^{m}$-open sets and $\alpha^{m}$-closed sets and studied some of their properties.