$\sigma$-compact Spaces in N$^{th}$-Topological Space

Authors

  • Ala Amourah Department of Mathematics, Faculty of Education and Arts, Sohar University, Sohar 3111, Sultanate of Oman,
  • Jamal Oudetallah Department of Mathematics, University of Petra, Amman, 11196, Jordan
  • Iqbal Batiha Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
  • Jamal Salah College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman
  • Mutaz Shatnawi Department of mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid 21110, Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5802

Keywords:

Tri-topological spaces;, Compactness;, Sigma compact spaces, Separation axioms

Abstract

The principal aims of this paper include the introduction of the concept of $\sigma$-compact Spaces in $n^{th}$-topological spaces, the definition of compactness, discussion of various generalizations encompassing compactness in $n^{th}$-topological space, the properties of $\sigma$-compact Spaces. Furthermore, our study extends to the analysis of the notion of countable compactness in $n^{th}$-topological spaces. Our investigation extends to various generalizations of these spaces.

Author Biographies

  • Ala Amourah, Department of Mathematics, Faculty of Education and Arts, Sohar University, Sohar 3111, Sultanate of Oman,

    Applied Science Research Center, Applied Science Private University, Amman, Jordan

  • Iqbal Batiha, Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan

    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Topology

License

Copyright (c) 2025 Ala Amourah, Jamal Oudetallah, Iqbal Batih, Jamal Salah, Mutaz Shatnawi

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How to Cite

$\sigma$-compact Spaces in N$^{th}$-Topological Space. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5802. https://doi.org/10.29020/nybg.ejpam.v18i2.5802