Towards a Unified Framework for Bioperations on $e^\star$-Open Sets in Topological Spaces

TL;DR

This paper introduces a new class of open sets and continuous functions in topological spaces, expanding the theoretical framework for bioperations and their properties.

Contribution

It presents a unified framework for bioperations on $e^ullet$-open sets and defines a novel class of continuous functions in topology.

Findings

Defined $e^ullet_{[eta,eta']}$-open sets and explored their properties

Introduced $(e^ullet_{[eta,eta']}, ext{ }e^ullet_{[eta,eta']})$-continuous functions and analyzed their characteristics

Provided foundational results for bioperations in topological spaces

Abstract

In this paper, we introduce the concept of $e^\star_{[\gamma,\gamma']}$-open sets in topological spaces and examine their properties in detail. Additionally, we propose a new class of functions, termed $(e^\star_{[\gamma,\gamma']},\ e^\star_{[\beta,\beta']})$-continuous functions, and explore their fundamental characteristics.