Volume 12, Issue 4 (April 2025), Pages: 19-23

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 Original Research Paper

On α-compact sets in ideal topological spaces

 Author(s): 

 Eman Almuhur ^1, *, Mona Khandaqji ¹, Mona Bin-Asfour ², Manal Al-Labadi ³, Wasim Audeh ³

 Affiliation(s):

 ¹Department of Mathematics, Faculty of Science, Applied Science Private University, Amman, Jordan
 ²Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
 ³Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-9837-4179

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2025.04.003

 Abstract

This paper examines the properties of α-continuous functions modulo (J, I) that map a countably α-compact ideal space (X, τ, J) to an ideal space (Y, σ, I), where Y is an α-closed subset of the Cartesian product (X × Y, τ × σ, J × I). It is shown that if (X, τ, J) has a weight of at least ℵ₀, it is the α-continuous image of a closed subspace of the cube D^{ℵ₀}. Additionally, an α-continuous function f: (X, τ, J) → (Y, σ, I), where Y is countably α-compact, can be extended under specific conditions. The concept of α-pseudocompactness is introduced in an ideal topological space (X, τ, J), and it is established that countably α-pseudocompactness is neither finitely multiplicative nor hereditary with respect to α-closed sets. Furthermore, it is proven that an α-continuous function modulo ideals mapping a Tychonoff ideal space to a countably α-pseudocompact space is perfect, and the Tychonoff space itself is countably α-pseudocompac.

 © 2025 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 α-continuous functions, Ideal topological spaces, α-pseudocompactness, Countably α-compact spaces, Tychonoff spaces

 Article history

 Received 2 November 2024, Received in revised form 6 March 2025, Accepted 7 April 2025

 Acknowledgment

The researchers acknowledge Applied Science Private University, University of Petra, Jordan, and Imam Mohammad Ibn Saud Islamic University, Saudi Arabia, for the full support granted to this research article.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Almuhur E, Khandaqji M, Bin-Asfour M, Al-Labadi M, and Audeh W (2025). On α-compact sets in ideal topological spaces. International Journal of Advanced and Applied Sciences, 12(4): 19-23

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