Araştırma Makalesi
Yıl 2024,
Sayı: 46, 51 - 70, 29.03.2024
Öz
This research deals with new operators $\wedge_{\Gamma}$, $\veebar_{\Gamma}$, and $\barwedge_{\Gamma}$, defined using $\Gamma$-local closure function and $\Psi_{\Gamma}$-operator in ideal topological spaces. It investigates the main features of these operators and their relationships with each other. The paper also analyzes their behaviors in some special ideals. Besides, it explores whether these operators preserve some set operations. Then, the study researches the properties of some special sets using these operators and proposes their characterizations. Additionally, it interprets some characterizations of the case cl$(\tau)\cap \Im=\{\emptyset\}$ and the closure compatibility by means of these new operators.
Anahtar Kelimeler
Ideal $\Gamma$-local closure function $\Psi_{\Gamma}$-operator
Destekleyen Kurum
The Office of Scientific Research Projects Coordination at Canakkale Onsekiz Mart University
Proje Numarası
FHD-2023-4505
Kaynakça
- K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
- R. Vaidyanathaswamy, The localisation theory in set-topology, Proceedings of the Indian Academy of Sciences - Section A 20 (1944) 51-61.
- D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly 97 (4) (1990) 295-310.
- T. Natkaniec, On I-continuity and I-semicontinuity points, Mathematica Slovaca 36 (3) (1986) 297-312.
- M. Mukherjee, N. R. Bishwambhar, R. Sen, On extension of topological spaces in terms of ideals, Topology and its Applications 154 (18) (2007) 3167-3172.
- T. R. Hamlett, D. Janković, Compatible extensions of ideals, Bollettino dell'Unione Matematica Italiana 7 (1992) 453-465.
- E. Ekici, A. N. Tunç, On $PC^{\star}$-closed sets, Journal of the Chungcheong Mathematical Society 29 (4) (2016) 565-572.
- E. Ekici, S. Özen, A generalized class of $\tau^{*}$ in ideal spaces, Filomat 27 (4) (2013) 529-535.
- Sk. Selim, T. Noiri, S. Modak, Some set-operators on ideal topological spaces, The Aligarh Bulletin of Mathematics 40 (1) (2021) 41-53.
- Sk. Selim, S. Modak, Md. M. Islam, Characterizations of Hayashi-Samuel spaces via boundary points, Communications in Advanced Mathematical Sciences 2 (3) (2019) 219-226.
- S. Modak, S. Selim, Set operators and associated functions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 (1) (2021) 456-467.
- A. Al-Omari, T. Noiri, Local closure functions in ideal topological spaces, Novi Sad Journal of Mathematics 43 (2) (2013) 139-149.
- A. Pavlovi$\acute{c}$, Local function versus local closure function in ideal topological spaces, Filomat 30 (14) (2016) 3725-3731.
- A. N. Tunç, S. Özen Yıldırım, A study on further properties of local closure functions, in: M. Öztürk (Ed.), 7th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2020), Muğla, 2020, pp. 123-123.
- A. N. Tunç, S. Özen Yıldırım, New sets obtained by local closure functions, Annals of Pure and Applied Mathematical Sciences 1 (1) (2021) 50-59.
- A. N. Tunç, S. Özen Yıldırım, $\Psi_{\Gamma}-C$ sets in ideal topological spaces, Turkish Journal of Mathematics and Computer Science 15 (1) (2023) 27-34.
- A. N. Tunç, S. Özen Yıldırım, On a topological operator via local closure function, Turkish Journal of Mathematics and Computer Science 15 (2) (2023) 227-236.
- N. S. Noorie, N. Goyal, On $S_{2\frac{1}{2}}$ mod I spaces and $\theta^{I}$-closed sets, International Journal of Mathematics Trends and Technology 52 (4) (2017) 226-228.
- N. V. Veličko, H-closed topological spaces, American Mathematical Society Translations 78 (2) (1968) 102-118.
- J. E. Joseph, $\theta$-closure and $\theta$-subclosed graphs, The Mathematical Chronicle 8 (1979) 99-117.
- M. Caldas, S. Jafari, M. M. Kovár, Some properties of $\theta$-open sets, Divulgaciones Matemáticas 12 (2) (2004) 161-169.
- N. Goyal, N. S. Noorie, $\theta$-closure and $T_{2\frac{1}{2}}$ spaces via ideals, Italian Journal of Pure and Applied Mathematics 41 (2019) 571-583.
Yıl 2024,
Sayı: 46, 51 - 70, 29.03.2024
Öz
Proje Numarası
FHD-2023-4505
Kaynakça
- K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
- R. Vaidyanathaswamy, The localisation theory in set-topology, Proceedings of the Indian Academy of Sciences - Section A 20 (1944) 51-61.
- D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly 97 (4) (1990) 295-310.
- T. Natkaniec, On I-continuity and I-semicontinuity points, Mathematica Slovaca 36 (3) (1986) 297-312.
- M. Mukherjee, N. R. Bishwambhar, R. Sen, On extension of topological spaces in terms of ideals, Topology and its Applications 154 (18) (2007) 3167-3172.
- T. R. Hamlett, D. Janković, Compatible extensions of ideals, Bollettino dell'Unione Matematica Italiana 7 (1992) 453-465.
- E. Ekici, A. N. Tunç, On $PC^{\star}$-closed sets, Journal of the Chungcheong Mathematical Society 29 (4) (2016) 565-572.
- E. Ekici, S. Özen, A generalized class of $\tau^{*}$ in ideal spaces, Filomat 27 (4) (2013) 529-535.
- Sk. Selim, T. Noiri, S. Modak, Some set-operators on ideal topological spaces, The Aligarh Bulletin of Mathematics 40 (1) (2021) 41-53.
- Sk. Selim, S. Modak, Md. M. Islam, Characterizations of Hayashi-Samuel spaces via boundary points, Communications in Advanced Mathematical Sciences 2 (3) (2019) 219-226.
- S. Modak, S. Selim, Set operators and associated functions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 (1) (2021) 456-467.
- A. Al-Omari, T. Noiri, Local closure functions in ideal topological spaces, Novi Sad Journal of Mathematics 43 (2) (2013) 139-149.
- A. Pavlovi$\acute{c}$, Local function versus local closure function in ideal topological spaces, Filomat 30 (14) (2016) 3725-3731.
- A. N. Tunç, S. Özen Yıldırım, A study on further properties of local closure functions, in: M. Öztürk (Ed.), 7th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2020), Muğla, 2020, pp. 123-123.
- A. N. Tunç, S. Özen Yıldırım, New sets obtained by local closure functions, Annals of Pure and Applied Mathematical Sciences 1 (1) (2021) 50-59.
- A. N. Tunç, S. Özen Yıldırım, $\Psi_{\Gamma}-C$ sets in ideal topological spaces, Turkish Journal of Mathematics and Computer Science 15 (1) (2023) 27-34.
- A. N. Tunç, S. Özen Yıldırım, On a topological operator via local closure function, Turkish Journal of Mathematics and Computer Science 15 (2) (2023) 227-236.
- N. S. Noorie, N. Goyal, On $S_{2\frac{1}{2}}$ mod I spaces and $\theta^{I}$-closed sets, International Journal of Mathematics Trends and Technology 52 (4) (2017) 226-228.
- N. V. Veličko, H-closed topological spaces, American Mathematical Society Translations 78 (2) (1968) 102-118.
- J. E. Joseph, $\theta$-closure and $\theta$-subclosed graphs, The Mathematical Chronicle 8 (1979) 99-117.
- M. Caldas, S. Jafari, M. M. Kovár, Some properties of $\theta$-open sets, Divulgaciones Matemáticas 12 (2) (2004) 161-169.
- N. Goyal, N. S. Noorie, $\theta$-closure and $T_{2\frac{1}{2}}$ spaces via ideals, Italian Journal of Pure and Applied Mathematics 41 (2019) 571-583.
Toplam 22 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Topoloji |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Proje Numarası | FHD-2023-4505 |
| Erken Görünüm Tarihi | 28 Mart 2024 |
| Yayımlanma Tarihi | 29 Mart 2024 |
| Gönderilme Tarihi | 12 Ocak 2024 |
| Kabul Tarihi | 23 Şubat 2024 |
| Yayımlandığı Sayı | Yıl 2024 Sayı: 46 |
Kaynak Göster
|