Abstract
In this study, we introduce the concepts of $(i,j)$-semi$^{*}$-$\Gamma $-open sets within the context of ideal bitopological spaces. This concept is demonstrated to be weaker than the established the notion of $(i,j)$-semi-$\Gamma $-open sets. Subsequently, we define strong $(i,j)$-semi$^{*}$-$\Gamma $-open sets in ideal bitopological spaces, elucidating some of their essential characteristics. Furthermore, leveraging this newly introduced concept, we establish the notions of strong $(i,j)$-semi$^{*}$-$\Gamma $-interior and strong $(i,j)$-semi$^{*}$-$\Gamma $-closure.
Keywords
Ideal bitopological spaces generalized open sets $(i j)$-$\Gamma $-open sets j)$-semi$^{*}$-$\Gamma $-open sets
References
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- J. Oudetallah, R. Alharbi, I. M. Batiha, On r-compactness in topological and bitopological spaces, Axioms 12 (2) (2023) 210 13 pages.
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- R. Vaidyanathaswamy, The localisation theory in set topology, Proceedings of the Indian Academy of Sciences 20 (1945) 51-61.
- D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly 97 (4) (1990) 295-310.
- E. Ekici, T. Noiri, *-Hyperconnected ideal topological spaces, Analele Sale Uviversitatii Alexandru Ioan Cuza Din Iasi-Seria Noua-Matematica 58 (1) (2012) 121-129.
- M. Çaldaş, S. Jafari, N. Rajesh, Some fundamental properties of $\beta$-open sets in ideal bitopological spaces, European Journal of Pure and Applied Mathematics 6 (2) (2013) 247-255.
- R. M. S.Aqeel, A. A. S. Bin-Kuddah, On strong semi\(^*\)-I-open sets in ideal topological spaces, University of Aden Journal of Natural and Applied Sciences 23 (2) (2019) 489-499.
- M. Çaldaş, S. Jafari, N. Rajesh, F. Smarandache, On I-open sets and I-continuous functions in ideal bitopological spaces, in: F. Smarandache (Ed.), Collected Papers (on Neutrosophics and Other Topics) Volume XIV, Global Knowledge Publishing House, Miami, 2022, 338-349.
- A. I. El-Maghrabi, M. Çaldaş, S. Jafari, R. M. Latif, A. Nasef, N. Rajesh, S. Shanthi, Properties of ideal bitopological $\alpha$-open sets, Scientific Studies and Research Series Mathematics and Informatics 27 (2) (2017) 15-36.
- N. Rajesh, M. Çaldaş, S. Jafari, Preopen sets in ideal bitopological spaces, Boletim da Sociedade Paranaense de Matemática 29 (2) (2011) 61-68.
Abstract
References
- A. Ghareeb, T. Noiri, $\Lambda$-Generalized closed sets with respect to an ideal bitopological space, Afrika Matematika 24 (2013) 97-101.
- D. J. Sarma, S. Acharjee, Some results on almost b-continuous functions in a bitopological space, Boletim da Sociedade Paranaense de Matemática 37 (2) (2019) 167-177.
- I. Bukhatwa, S. Demiralp, On generalized $\beta$-open sets in ideal bitopological space, European Journal of Pure and Applied Mathematics 13 (2) (2020) 269-279.
- I. Bukhatwa, S. Demiralp, On some generalized open sets in ieal bitopological spaces, Journal of New Theory (32) (2020) 1-10.
- J. Oudetallah, R. Alharbi, I. M. Batiha, On r-compactness in topological and bitopological spaces, Axioms 12 (2) (2023) 210 13 pages.
- T. Noiri, N. Rajesh, Generalized closed sets with respect to an ideal in bitopological spaces, Acta Mathematica Hungarica 125 (1-2) (2009) 17-20.
- R. Vaidyanathaswamy, The localisation theory in set topology, Proceedings of the Indian Academy of Sciences 20 (1945) 51-61.
- D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly 97 (4) (1990) 295-310.
- E. Ekici, T. Noiri, *-Hyperconnected ideal topological spaces, Analele Sale Uviversitatii Alexandru Ioan Cuza Din Iasi-Seria Noua-Matematica 58 (1) (2012) 121-129.
- M. Çaldaş, S. Jafari, N. Rajesh, Some fundamental properties of $\beta$-open sets in ideal bitopological spaces, European Journal of Pure and Applied Mathematics 6 (2) (2013) 247-255.
- R. M. S.Aqeel, A. A. S. Bin-Kuddah, On strong semi\(^*\)-I-open sets in ideal topological spaces, University of Aden Journal of Natural and Applied Sciences 23 (2) (2019) 489-499.
- M. Çaldaş, S. Jafari, N. Rajesh, F. Smarandache, On I-open sets and I-continuous functions in ideal bitopological spaces, in: F. Smarandache (Ed.), Collected Papers (on Neutrosophics and Other Topics) Volume XIV, Global Knowledge Publishing House, Miami, 2022, 338-349.
- A. I. El-Maghrabi, M. Çaldaş, S. Jafari, R. M. Latif, A. Nasef, N. Rajesh, S. Shanthi, Properties of ideal bitopological $\alpha$-open sets, Scientific Studies and Research Series Mathematics and Informatics 27 (2) (2017) 15-36.
- N. Rajesh, M. Çaldaş, S. Jafari, Preopen sets in ideal bitopological spaces, Boletim da Sociedade Paranaense de Matemática 29 (2) (2011) 61-68.
Details
| Primary Language | English |
|---|---|
| Subjects | Topology |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | March 28, 2024 |
| Publication Date | March 29, 2024 |
| Submission Date | February 23, 2024 |
| Acceptance Date | March 27, 2024 |
| Published in Issue | Year 2024 Issue: 46 |
