Araştırma Makalesi
Yıl 2023,
Cilt: 15 Sayı: 1, 27 - 34, 30.06.2023
Öz
In this paper, we present a new type of set called $\Psi_{\Gamma}-C$ set by using the operator $\Psi_{\Gamma}$. We investigate the relationships of these sets with some special sets which were studied in the literature. For instance $\theta$-open set, semi $\theta$-open set, $\theta$-semiopen set, regular $\theta$-closed set. In particular, we show that $\Psi_{\Gamma}-C$ set is weaker than $\theta$-open set. Furthermore, we prove that the collection of $\Psi_{\Gamma}-C$ set is closed under arbitrary union. Finally, we obtain the conclusion that the collection of $\Psi_{\Gamma}-C$ set forms a supratopology.
Anahtar Kelimeler
$\Psi_{\Gamma}-C$ set local closure function $\theta$-closed set $L_{\Gamma}$-perfect set
Destekleyen Kurum
-
Proje Numarası
-
Teşekkür
-
Kaynakça
- Al-Omari, A., Noiri, T., Local closure functions in ideal topological spaces, Novi Sad J. Math., 43(2)(2013), 139–149.
- Amsaveni, V., Anitha, M., Subramanian, A., New types of semi-open sets, International Journal of New Innovations in Engineering and Technology, 9(4)(2019), 14–17.
- Bandyopadhyay, C., Modak, S., A new topology via $\Psi$-operator, Proc. Nat. Acad. Sci. India, 76(4)(2006), 317–320.
- Caldas, M., Ganster, M., Georgiou, D. N., Jafari, S., Noiri, T., On $\theta$-semiopen sets and separation axioms in topological spaces, Carpathian J. Math., 24(1)(2008), 13–22.
- Devika, A., Thilagavathi, A., $M^{\ast}$-open sets in topological spaces, International Journal of Mathematics and Its Applications, 4(1-B)(2016), 1–8.
- Islam, Md. M., Modak, S., Operators associated with the $*$ and $\psi$ operators, J. Taibah Univ. Sci., 12(4)(2018), 444–449.
- Islam, Md. M., Modak, S., Second approximation of local functions in ideal topological spaces, Acta Comment. Univ. Tartu. Math., 22(2)(2018), 245–256.
- Kuratowski, K., Topology, Vol. I, Academic Press, New York, 1966.
- Levine, N., Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(1970), 89–96.
- Mashhour, A.S., Abd El-Monsef, M. E., El-Deeb, S.N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47–53.
- Mashhour, A.S., Allam, A. A., Mahmoud, F.S., Khedr, F.H., On supratopological spaces, Indian J. Pure and Appl. Math., 14(4)(1983), 502–510.
- Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci., 82(3)(2012), 233–243.
- Modak, S., Bandyopadhyay, C., A note on $\Psi$-operator, Bull. Malays. Math. Sci. Soc. (2), 30(1)(2007), 43–48.
- Natkaniec, T., On I-continuity and I-semicontinuity points, Mathematica Slovaca, 36(3)(1986), 297–312.
- Noorie, N.S., Goyal, N., 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.
- Pavlovic, A., Local function versus local closure function in ideal topological spaces, Filomat, 30(14)(2016), 3725–3731.
- Tunç, A.N., O¨ zen Yıldırım, S., A study on further properties of local closure functions, 7th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2020), (2020), 123–123.
- Tunç, A.N., Özen Yıldırım, S., New sets obtained by local closure functions, Annals of Pure and Applied Mathematical Sciences, 1(1)(2021), 50–59.
- Velicko, N.V., H-closed topological spaces, Mat. Sb. (N.S.), 70(112)(1966), 98–112. English transl., Amer. Math. Soc. Transl., 78(2)(1968), 102–118.
Yıl 2023,
Cilt: 15 Sayı: 1, 27 - 34, 30.06.2023
Öz
Proje Numarası
-
Kaynakça
- Al-Omari, A., Noiri, T., Local closure functions in ideal topological spaces, Novi Sad J. Math., 43(2)(2013), 139–149.
- Amsaveni, V., Anitha, M., Subramanian, A., New types of semi-open sets, International Journal of New Innovations in Engineering and Technology, 9(4)(2019), 14–17.
- Bandyopadhyay, C., Modak, S., A new topology via $\Psi$-operator, Proc. Nat. Acad. Sci. India, 76(4)(2006), 317–320.
- Caldas, M., Ganster, M., Georgiou, D. N., Jafari, S., Noiri, T., On $\theta$-semiopen sets and separation axioms in topological spaces, Carpathian J. Math., 24(1)(2008), 13–22.
- Devika, A., Thilagavathi, A., $M^{\ast}$-open sets in topological spaces, International Journal of Mathematics and Its Applications, 4(1-B)(2016), 1–8.
- Islam, Md. M., Modak, S., Operators associated with the $*$ and $\psi$ operators, J. Taibah Univ. Sci., 12(4)(2018), 444–449.
- Islam, Md. M., Modak, S., Second approximation of local functions in ideal topological spaces, Acta Comment. Univ. Tartu. Math., 22(2)(2018), 245–256.
- Kuratowski, K., Topology, Vol. I, Academic Press, New York, 1966.
- Levine, N., Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(1970), 89–96.
- Mashhour, A.S., Abd El-Monsef, M. E., El-Deeb, S.N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47–53.
- Mashhour, A.S., Allam, A. A., Mahmoud, F.S., Khedr, F.H., On supratopological spaces, Indian J. Pure and Appl. Math., 14(4)(1983), 502–510.
- Modak, S., Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci., 82(3)(2012), 233–243.
- Modak, S., Bandyopadhyay, C., A note on $\Psi$-operator, Bull. Malays. Math. Sci. Soc. (2), 30(1)(2007), 43–48.
- Natkaniec, T., On I-continuity and I-semicontinuity points, Mathematica Slovaca, 36(3)(1986), 297–312.
- Noorie, N.S., Goyal, N., 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.
- Pavlovic, A., Local function versus local closure function in ideal topological spaces, Filomat, 30(14)(2016), 3725–3731.
- Tunç, A.N., O¨ zen Yıldırım, S., A study on further properties of local closure functions, 7th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2020), (2020), 123–123.
- Tunç, A.N., Özen Yıldırım, S., New sets obtained by local closure functions, Annals of Pure and Applied Mathematical Sciences, 1(1)(2021), 50–59.
- Velicko, N.V., H-closed topological spaces, Mat. Sb. (N.S.), 70(112)(1966), 98–112. English transl., Amer. Math. Soc. Transl., 78(2)(1968), 102–118.
Toplam 19 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Proje Numarası | - |
| Yayımlanma Tarihi | 30 Haziran 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 15 Sayı: 1 |