Modifications to Mixed θ(ν1, ν2)-open Sets inGeneralized Topological Spaces

Authors

  • Abdo Qahis Department of Mathematics, Faculty of Science and Arts, Nagran university, Saudi Arabia.
  • Awn Alqahtani Najran university

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5475

Keywords:

γθ(ν1,ν2) operation , θ(ν1, ν2)-open sets, γ˜θ(ν1,ν2) operation, ˜θ(ν1, ν2)- open set, G(ν1, ν2)-regularity.

Abstract

A. Cs´asz´ar and Makai Jr. [5] introduced the concepts of the mixed operation γθ(ν1,ν2) and mixed θ(ν1, ν2)-open sets in generalized topological spaces. In this paper, we extend this framework by introducing the concepts of mixed operation γ˜θ(ν1,ν2) and mixed ˜θ(ν1, ν2)-open sets (briefly, ˜θ(ν1, ν2)- open sets) and investigate their fundamental properties in generalized topological spaces. We explore the relationships among γ˜θ(ν1,ν2), γθ(ν1,ν2), and γθ(ν), as well as the relationships among ˜θ(ν1, ν2)-open sets, θ(ν1, ν2)-open sets, and μ-open sets. Additionally, we introduce the notion of G(ν1, ν2)-regularity in generalized topological spaces. Finally, we provide characterizations of ˜θ(ν1, ν2)-open sets using mixed G(ν1, ν)-regular concept

Author Biography

  • Abdo Qahis, Department of Mathematics, Faculty of Science and Arts, Nagran university, Saudi Arabia.
    Department of Mathematics

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Published

2024-10-31

Issue

Vol. 17 No. 4: (October 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 Abdo Qahis, Awn Alqahtani

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How to Cite

Modifications to Mixed θ(ν1, ν2)-open Sets inGeneralized Topological Spaces. (2024). European Journal of Pure and Applied Mathematics, 17(4), 3610-3621. https://doi.org/10.29020/nybg.ejpam.v17i4.5475