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Gαω-Open sets in Grill Topological Spaces

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2021
Amin Saif, A. Mahdi, Khaled M. Hamadi

Amin Saif, A Mahdi and Khaled M Hamadi. G???Open sets in Grill Topological Spaces. International Journal of Computer Applications 183(13):1-5, July 2021. BibTeX

	author = {Amin Saif and A. Mahdi and Khaled M. Hamadi},
	title = {G???Open sets in Grill Topological Spaces},
	journal = {International Journal of Computer Applications},
	issue_date = {July 2021},
	volume = {183},
	number = {13},
	month = {Jul},
	year = {2021},
	issn = {0975-8887},
	pages = {1-5},
	numpages = {5},
	url = {},
	doi = {10.5120/ijca2021921446},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


In this paper, we investigate and introduce new class of open sets in grill topological spaces, class of Gαω-open sets, which is weak form of the class of Gα-open sets and strong form of class of Gω-open sets. We give the relationship of this notion with the other known sets and introduce the notions of the closure operator and the interior operator of Gαω-open sets.


  1. A. Saif, M. Al-Hawmi and B. Al-refaei, On Gω-open sets in grill topological spaces, n6 Journal of Advance in Mathematics and Computer Science, 35(6), (2020), 132-143.
  2. H. Z. Hdeib, ω-closed mappings, Revista Colombiana de Matematicas, 16 (1982), 65-78.
  3. F. Helen, 1968, Introduction to General Topology, Boston: University of Massachusetts.
  4. T. Noiri, A. Al-omari and M. Noorani, Weak forms of ω-open sets and decompositions of continuity, European Journal of Pure and Applied Mathematics 1, (2009), 73-84.
  5. O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970.
  6. G. Choquet; Sur les notions de filtre et grille, Comptes Rendus Acad. Sci. Paris, 224 (1947), 171-173.
  7. B. Roy and M. N. Mukherjee; On a typical topology induced by a grill, Soochow J. Math., 33 (2007), 771-786.
  8. A. Al-Omari and T. Noiri, Characterizations of strongly compact spaces, Int. J. Math. and Math. Sciences, ID 573038 (2009), 1-9.
  9. O. Ravi, I. Rajasekaran, S. Kanna and M. Paranjothi, New Generalized Classes of??. European Journal of Pure and Applied Mathematics. Vol. 9, No. 2, (2016), 152-164.


Open set; Open set; α-Open set; ω-Open set; Grill topological space