ON ANTI-WEAK STRUCTURES | ||||
| Bulletin of Faculty of Science, Zagazig University | ||||
| Article 11, Volume 2025, Issue 3, July 2025, Page 120-129 PDF (894.46 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/bfszu.2024.342938.1454 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
samir abdelmageed farag  1; Hassan M. Abu-Donia2
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| 1Basic Science Department, Modern Academy for Engineering and Technology, Egypt | ||||
| 2Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt | ||||
| Abstract | ||||
| We introduce the concept of an anti-weak structure, which naturally generalizes to include anti-minimal and anti-topological spaces. Within this framework, we explore several key notions such as ϖ-exterior, ϖ-boundary, ϖ-dense, ϖ-nowhere dense, and ϖ-rare sets. These concepts are crucial for understanding the broader implications of anti-weak structures. Additionally, we delve into various structural components, including π(ϖ), σ(ϖ), α(ϖ), β(ϖ), ρ(ϖ), ro(ϖ), and rc(ϖ), examining their respective properties in detail. This detailed exploration helps in comprehending the intricate nature of these components and their interactions within the framework. Furthermore, we present the idea of a ϖ-subspace, analyzing its associated characteristics to provide a comprehensive understanding of its role and significance. Finally, we define and study the concept of a (ϖ, ϖ')-anti-weak continuous function. This function is essential for establishing the relevance and applicability of anti-weak structures within this generalized framework. By examining these functions, we can better understand their behavior and significance in various contexts, thereby enriching the overall theory of anti-weak structures. | ||||
| Keywords | ||||
| $-exterior; $-boundary; $-dense; $-nowhere dense | ||||
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