On Nearly α-Compact Topological Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6543Keywords:
α-continuous function, α-open set, topological spaces, nearly α-compact topologicalAbstract
In this paper, we introduce and investigate the concept of nearly α-compact topological spaces as a natural generalization of α-compact and countably α-compact spaces. We establish fundamental properties and characterizations of nearly α-compact spaces, demonstrating their relationship with various topological properties including α-continuity, separation axioms, and compactness-like properties. Several equivalent conditions for nearly α-compactness are provided, and we prove that the property is preserved under certain types of mappings. The behavior of nearly α-compact spaces under topological operations such as subspaces, products, and sums is thoroughly examined. We also introduce the notion of α-nearness and investigate its connection with nearly α-compact spaces. Additionally, we provide comprehensive examples and establish new theorems that demonstrate the richness and applicability of this concept.
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Copyright (c) 2025 Jamal Oudetallah, Ahmad Almalkawi, Ala Amourah, Abdullah Alsoboh, Khaled Al Mashrafi, Tala Sasa
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