Some Variants of Ĉech Δ-Normal Closure Space | ||||
| Bulletin of Faculty of Science, Zagazig University | ||||
| Article 10, Volume 2025, Issue 3, July 2025, Page 112-119 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/bfszu.2024.342900.1453 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Hassan M. Abu-Donia1; waheed mohamed amin   2; Rodyna hosny3
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| 1Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt | ||||
| 2Zagazig University | ||||
| 3Department 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. | ||||
| Keywords | ||||
| Ĉech closure space; Ĉech δ- closed set; Ĉech π-closed set; Ĉech Δ-normal (Ĉech weakly Δ-normal) spaces | ||||
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