G-Compact Spaces Characterized by the Intersection of Countable Neighborhoods

Authors

  • Mutaz Shatnawi Department of mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid 21110, Jordan
  • Jamal Oudetallah Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, 11196, Jordan
  • Anwar Bataiha Department of mathematics, Faculty of Science, Jadara University, Irbid 21110, Jordan
  • Ala Amourah Faculty of Education and Arts, Mathematics Section, Sohar University,Sohar 3111, Sultanat of Oman
  • Abdullah Alsoboh College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra
  • Tala Sasa Department of Mathematics, Faculty of Science, Applied Science Private University, 15 Amman, Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6067

Keywords:

compact space, Lindel$\ddot{o}$f space, countably compact space, G-compact space, G-Lindel$\ddot{o}$f space, G-countably compact, separation axioms, G-separation axioms

Abstract

 In this research, we introduce and analyze the concepts of \(G\)-compactness, \(G\)-Lindel$\ddot{o}$fness, and \(G\)-countably compactness within the framework of topological spaces, which are characterized by more rigorous conditions compared to those governing compact and Lindel$\ddot{o}$f spaces. We formulate a series of theorems and present a variety of examples to clarify the relationships among \(G\)-compactness, \(G\)-Lindel$\ddot{o}$fness, compactness, and Lindel$\ddot{o}$fness. Additionally, we define the \(G\)-separation axioms utilizing $G_\delta$ sets and explore the interrelations among these concepts.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Topology

License

Copyright (c) 2025 Mutaz Shatnawi; Jamal Oudetallah; Anwar Bataiha, Ala Amourah, Abdullah Alsoboh, Tala Sasa

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How to Cite

G-Compact Spaces Characterized by the Intersection of Countable Neighborhoods. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6067. https://doi.org/10.29020/nybg.ejpam.v18i3.6067