Some Variants of Ĉech Δ-Normal Closure Space

Document Type : Original Article

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1 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

2 Zagazig University

3 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig

Abstract

This manuscript investigates several generalized notions of Ĉech normality within the framework of Ĉech closure spaces. The study delves into different types of Ĉech normality that lie between Ĉech Δ-normal and Ĉech κ-normal spaces. By systematically analyzing these variations, it establishes the relationships between them and provides examples to clarify and support the findings. The concept of Ĉech β-normal space plays a central role, serving as a foundation to introduce innovative decompositions of normality. These decompositions offer new insights into the structural properties of Ĉech closure spaces, enhancing the theoretical framework of topological normality. Through rigorous examination, the distinctions, properties, and interconnections among the studied forms of Ĉech normality are highlighted, emphasizing their mathematical significance and potential applications. This work represents a significant contribution to the field by advancing the understanding of Ĉech spaces and their complex normality structures, while also paving the way for future research in related mathematical theories and frameworks.

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