Research Article
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On Grill S<sub>p</sub>-Open Set in Grill Topological Spaces

Year 2018, Issue: 23, 85 - 92, 01.06.2018

Abstract

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.

References

  • [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.
Year 2018, Issue: 23, 85 - 92, 01.06.2018

Abstract

References

  • [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.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Dhanabal Saravanakumar

Nagarajan Kalaivani This is me

Publication Date June 1, 2018
Submission Date March 19, 2018
Published in Issue Year 2018 Issue: 23

Cite

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. June 2018;(23):85-92.
Chicago Saravanakumar, Dhanabal, and Nagarajan Kalaivani. “On Grill Sp-Open Set in Grill Topological Spaces”. Journal of New Theory, no. 23 (June 2018): 85-92.
EndNote Saravanakumar D, Kalaivani N (June 1, 2018) On Grill Sp-Open Set in Grill Topological Spaces. Journal of New Theory 23 85–92.
IEEE D. Saravanakumar and N. Kalaivani, “On Grill Sp-Open Set in Grill Topological Spaces”, JNT, no. 23, pp. 85–92, June 2018.
ISNAD Saravanakumar, Dhanabal - Kalaivani, Nagarajan. “On Grill Sp-Open Set in Grill Topological Spaces”. Journal of New Theory 23 (June 2018), 85-92.
JAMA Saravanakumar D, Kalaivani N. On Grill Sp-Open Set in Grill Topological Spaces. JNT. 2018;:85–92.
MLA Saravanakumar, Dhanabal and Nagarajan Kalaivani. “On Grill Sp-Open Set in Grill Topological Spaces”. Journal of New Theory, no. 23, 2018, pp. 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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