Strong Forms of Weakly e-continuous Functions

TL;DR

This paper introduces two new classes of continuity, eR-continuous and weakly eR-continuous functions, based on e-regular sets, and explores their properties and relationships with existing continuity concepts.

Contribution

It defines and characterizes two stronger forms of weakly e-continuity, expanding the theoretical framework of continuity via e-regular sets.

Findings

Introduced eR-continuous and weakly eR-continuous functions

Provided characterizations of weakly eR-continuous functions

Explored relations with other continuity types

Abstract

The main purpose of this study is to introduce and study two new classes of continuity called eR-continuous functions and weakly eR-continuous functions via e-regular sets. Both of the forms of continuous functions we have described are stronger than the weakly e-continuity. Furthermore, we obtain various characterizations of weakly eR-continuous functions. In addition, we examine not only the relations of these functions with some other forms of existing continuous functions, but also some of their fundamental properties.