Abstract
In this study, we first define the concept of neutrosophic beta-open set. Then, using this new set definition, we present neutrosophic beta-compact and neutrosophic beta-closed spaces and examine their properties. Also, we classify these spaces using the concept of neutrosophic filterbase, which is introduced for the first time in this study. And, relationships between these different types and forms of compactness are investigated.
Keywords
Neutrosophic Beta-open set, Neutrosophic Beta-Compactness Neutrosophic Beta-closed Space Neutrosophic Filterbases
References
- M.E. Abd El-Monsef, S.N. El-Deeb, and R.A. Mahmoud, β-open sets and β-continuous Mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983) 77-90.
- A. Acikgoz, H. Cakalli, F. Esenbel, and Lj.D.R. Kočinac, A quest of G-continuity in neutrosophic spaces, Math. Meth. Appl. Sci. 44 (9) (2021) 7834-7844.
- A. Acikgoz, and F. Esenbel, Neutrosophic Connected topological spaces, Fasc. Math. 66 (2023) 5-22.
- A. Acikgoz, F. Esenbel and O. Mucuk, Neutrosophication β-Compactness, Seventh International Conference of Mathematical Sciences (ICMS 2023) Abstract Book page 17 Maltepe University Istanbul Turkey.
- A. Acikgoz, and F. Esenbel F. Neutrosophic seperation axioms, Maltepe J Math. 5(2), (2023) 32–40.
- B. Ganesan, On fuzzy β-compact spaces and fuzzy β-extremally disconnected spaces, Kybernetika [cybernetics] 33(3) (1997) 271-277.
- R. Dhavaseelan, S. Jafari, C. Ozel, and C.M. A Al-Shumrani, Generalized neutrosophic contra-continuity, In: F Smarandache, S Pramanik, eds. New Trends in Neutrosophic Theory and Applications Vol. II (2018) 365-380.
- I.M. Hanafy, Fuzzy β-Compactness and Fuzzy β-Closed Spaces, Turk J Math. 28 (2004) 281–293.
- A.A. Salama, and S.A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR J. Math. 3 (2012) 31-35.
- F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24 (2005) 287-297.
Abstract
References
- M.E. Abd El-Monsef, S.N. El-Deeb, and R.A. Mahmoud, β-open sets and β-continuous Mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983) 77-90.
- A. Acikgoz, H. Cakalli, F. Esenbel, and Lj.D.R. Kočinac, A quest of G-continuity in neutrosophic spaces, Math. Meth. Appl. Sci. 44 (9) (2021) 7834-7844.
- A. Acikgoz, and F. Esenbel, Neutrosophic Connected topological spaces, Fasc. Math. 66 (2023) 5-22.
- A. Acikgoz, F. Esenbel and O. Mucuk, Neutrosophication β-Compactness, Seventh International Conference of Mathematical Sciences (ICMS 2023) Abstract Book page 17 Maltepe University Istanbul Turkey.
- A. Acikgoz, and F. Esenbel F. Neutrosophic seperation axioms, Maltepe J Math. 5(2), (2023) 32–40.
- B. Ganesan, On fuzzy β-compact spaces and fuzzy β-extremally disconnected spaces, Kybernetika [cybernetics] 33(3) (1997) 271-277.
- R. Dhavaseelan, S. Jafari, C. Ozel, and C.M. A Al-Shumrani, Generalized neutrosophic contra-continuity, In: F Smarandache, S Pramanik, eds. New Trends in Neutrosophic Theory and Applications Vol. II (2018) 365-380.
- I.M. Hanafy, Fuzzy β-Compactness and Fuzzy β-Closed Spaces, Turk J Math. 28 (2004) 281–293.
- A.A. Salama, and S.A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR J. Math. 3 (2012) 31-35.
- F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24 (2005) 287-297.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics (Other) |
| Journal Section | Research Article |
| Authors | |
| Submission Date | July 12, 2024 |
| Acceptance Date | September 20, 2024 |
| Early Pub Date | November 6, 2024 |
| Publication Date | November 8, 2024 |
| Published in Issue | Year 2024 Volume: 6 Issue: 2 |
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