Araştırma Makalesi
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On Grill S<sub>p</sub>-Open Set in Grill Topological Spaces

Yıl 2018, Sayı: 23, 85 - 92, 01.06.2018

Dhanabal Saravanakumar , Nagarajan Kalaivani

Öz

In this paper, we introduce a new type of grill set
namely; G-open sets, which is
analogous to the G-semiopen sets in a grill topological space (X,t,G).  Further, we define G-continuous and G-open functions by using a G-open set and we investigate some
of their important properties.

Anahtar Kelimeler

Gs_p-open set Gs_p O(X) Gs_p-continuous function Gs_p-open function

Kaynakça

  • [1] M. E. Abd El-Monsef and A. M. Kozae, Some generalized forms of compactness and closeness, Delta J. Sci., 9 (2) (1985), 257-269.
  • [2] G. Choquet, Sur les notions de filtre et grille, Comptes Rendus Acad. Sci. Paris, 224 (1947), 171-173.
  • [3] E. Hatir and S. Jafari, On some new classes of sets and a new decomposition of continuity via grills, J. Adv. Math. Studies, 3 (1) (2010), 33-40.
  • [4] Talal Al-Hawary and A. Al-Omari, ω-continuous like mappings, Al-Manarah J. 13(6) (2007),135-147.
  • [5] T. A. Al-Hawary-with A. Al-Omari, Decompositions of Continuity, Turkish J. Math., 30(20)(2006). 187-195.
  • [6] Talal Al-Hawary and A. Al-Omari, Between open and ω-open sets, Q &A in General Topology 24, 67-77, 2006.
  • [7] T. A. Al-Hawary, On Generalized preopen sets, Proyecciones: revista de matematica 31(4) (2013), 63-76.
  • [8] T. Al-Hawary, ρ-closed sets, Acta Universitatis aplulensis 35(2013), 29-36.
  • [9] T. Al-Hawary, Decompositions of continuity via ζ-open sets, Acta Universitatis aplulensis 34(2013), 137-142.
  • [10] K. Kuratowski, Topologie, Warsazawa, 1933.
  • [11] N. Levine, A decomposition of continuity in topological spaces, Amer Math. Monthly, 68 (1961), 36-41.
  • [12] N. Levine, Semiopen sets and semicontinuity in topological spaces, Amer. Math. Monthly, 70 (1993), 36-41.
  • [13] D. Mandal and M. N. Mukerjee, On a class of sets via grill: A decomposition of continuity, An. St. Univ. Ovidius Constanta, 20 (2012), 307-316.
  • [14] A. S. Mashhour, M. E. Abd EL-Monsef, and S. N. El-Deep, On pre-continuous and weak pre-continuous mappings, Proc. Math. and Phys. Soc. Egypt, 53 (1982), 47-53.
  • [15] O. Nijastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970.
  • [16] A. Al-Omari and T. Noiri, Decompositions of continuity via grills, Jordan J. Mat. Stat. 4 (2011) 33-46.
  • [17] B. Roy and M. N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math., 33 (4) (2007), 771-786.
  • [18] B. Roy and M. N. Mukherjee, Concerning topologies induced by principal grills, An. Stiint. Univ. AL. I. Cuza Iasi. Mat. (N. S.), 55 (2) (2009), 285-294.
  • [19] W. J. Thron, Proximity structure and grills, Math. Ann., 206 (1973), 35-62.

Yıl 2018, Sayı: 23, 85 - 92, 01.06.2018

Dhanabal Saravanakumar , Nagarajan Kalaivani

Öz

Kaynakça

  • [1] M. E. Abd El-Monsef and A. M. Kozae, Some generalized forms of compactness and closeness, Delta J. Sci., 9 (2) (1985), 257-269.
  • [2] G. Choquet, Sur les notions de filtre et grille, Comptes Rendus Acad. Sci. Paris, 224 (1947), 171-173.
  • [3] E. Hatir and S. Jafari, On some new classes of sets and a new decomposition of continuity via grills, J. Adv. Math. Studies, 3 (1) (2010), 33-40.
  • [4] Talal Al-Hawary and A. Al-Omari, ω-continuous like mappings, Al-Manarah J. 13(6) (2007),135-147.
  • [5] T. A. Al-Hawary-with A. Al-Omari, Decompositions of Continuity, Turkish J. Math., 30(20)(2006). 187-195.
  • [6] Talal Al-Hawary and A. Al-Omari, Between open and ω-open sets, Q &A in General Topology 24, 67-77, 2006.
  • [7] T. A. Al-Hawary, On Generalized preopen sets, Proyecciones: revista de matematica 31(4) (2013), 63-76.
  • [8] T. Al-Hawary, ρ-closed sets, Acta Universitatis aplulensis 35(2013), 29-36.
  • [9] T. Al-Hawary, Decompositions of continuity via ζ-open sets, Acta Universitatis aplulensis 34(2013), 137-142.
  • [10] K. Kuratowski, Topologie, Warsazawa, 1933.
  • [11] N. Levine, A decomposition of continuity in topological spaces, Amer Math. Monthly, 68 (1961), 36-41.
  • [12] N. Levine, Semiopen sets and semicontinuity in topological spaces, Amer. Math. Monthly, 70 (1993), 36-41.
  • [13] D. Mandal and M. N. Mukerjee, On a class of sets via grill: A decomposition of continuity, An. St. Univ. Ovidius Constanta, 20 (2012), 307-316.
  • [14] A. S. Mashhour, M. E. Abd EL-Monsef, and S. N. El-Deep, On pre-continuous and weak pre-continuous mappings, Proc. Math. and Phys. Soc. Egypt, 53 (1982), 47-53.
  • [15] O. Nijastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970.
  • [16] A. Al-Omari and T. Noiri, Decompositions of continuity via grills, Jordan J. Mat. Stat. 4 (2011) 33-46.
  • [17] B. Roy and M. N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math., 33 (4) (2007), 771-786.
  • [18] B. Roy and M. N. Mukherjee, Concerning topologies induced by principal grills, An. Stiint. Univ. AL. I. Cuza Iasi. Mat. (N. S.), 55 (2) (2009), 285-294.
  • [19] W. J. Thron, Proximity structure and grills, Math. Ann., 206 (1973), 35-62.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Dhanabal Saravanakumar

Nagarajan Kalaivani

Yayımlanma Tarihi 1 Haziran 2018
Gönderilme Tarihi 19 Mart 2018
Yayımlandığı Sayı Yıl 2018 Sayı: 23

Kaynak Göster

APA Saravanakumar, D., & Kalaivani, N. (2018). On Grill Sp-Open Set in Grill Topological Spaces. Journal of New Theory(23), 85-92.
AMA Saravanakumar D, Kalaivani N. On Grill Sp-Open Set in Grill Topological Spaces. JNT. Haziran 2018;(23):85-92.
Chicago Saravanakumar, Dhanabal, ve Nagarajan Kalaivani. “On Grill Sp-Open Set in Grill Topological Spaces”. Journal of New Theory, sy. 23 (Haziran 2018): 85-92.
EndNote Saravanakumar D, Kalaivani N (01 Haziran 2018) On Grill Sp-Open Set in Grill Topological Spaces. Journal of New Theory 23 85–92.
IEEE D. Saravanakumar ve N. Kalaivani, “On Grill Sp-Open Set in Grill Topological Spaces”, JNT, sy. 23, ss. 85–92, Haziran 2018.
ISNAD Saravanakumar, Dhanabal - Kalaivani, Nagarajan. “On Grill Sp-Open Set in Grill Topological Spaces”. Journal of New Theory 23 (Haziran 2018), 85-92.
JAMA Saravanakumar D, Kalaivani N. On Grill Sp-Open Set in Grill Topological Spaces. JNT. 2018;:85–92.
MLA Saravanakumar, Dhanabal ve Nagarajan Kalaivani. “On Grill Sp-Open Set in Grill Topological Spaces”. Journal of New Theory, sy. 23, 2018, ss. 85-92.
Vancouver Saravanakumar D, Kalaivani N. On Grill Sp-Open Set in Grill Topological Spaces. JNT. 2018(23):85-92.


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