Volume 11, Issue 9 (September 2024), Pages: 121-125

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 Original Research Paper

Strongly D_α^p-closed graphs in bitopological spaces

 Author(s): 

 Eman Almuhur ^1, *, Manal Al-Labadi ², Maysoon Qousini ³, Raeesa Bashir ⁴

 Affiliation(s):

 ¹Department of Mathematics, Faculty of Science, Applied Science Private University, Amman, Jordan
 ²Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan
 ³Department of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, Amman, Jordan
 ⁴Department of Mathematics, National Institute of Technology, Jammu and Kashmir, India

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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.2024.09.013

 Abstract

In this paper, we introduce the concepts of D^p_α −open, D^p_α −closed subsets, pairwise-α-closed, pairwise-g-closed subsets, pairwise-strongly α-closed graph G(f) and strongly D^p_α −closed graph of bitopological spaces. We showed that each closed graph is D^p_α −closed. In addition, the concepts of D^p_α −continuous, open, and closed functions are defined, and the relations between τ_p-α, τ_p-g, and  D^p_α −continuous functions are clarified. The fact that strongly D^p_α −closed graph is D^p_α −closed is illustrated. We studied when the graph G(f) is p-strongly closed and p-D_α-closed subsets of the bitopological space (X,τ₁,τ₂). Moreover, the notions of Dⁱ_α −interior of a subset of X and Dⁱ_α −closure are defined.

 © 2024 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

 D^p_α −open, D^p_α −closed, Bitopological spaces, D^p_α −continuous functions, Graph 𝐺(𝑓)

 Article history

 Received 17 May 2024, Received in revised form 4 September 2024, Accepted 6 September 2024

 Acknowledgment

The authors are grateful to the anonymous reviewers for their valuable comments.

 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, Al-Labadi M, Qousini M, and Bashir R (2024). Strongly D^p_α-closed graphs in bitopological spaces. International Journal of Advanced and Applied Sciences, 11(9): 121-125

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