On some topological concepts via grill

Document Type : Research Paper


Department of Mathematics College of Education for Pure Science, Ibn Al-Haitham University of Baghdad, Iraq


In this work, the new grill concepts are studied using grill topological spaces and by using some defined sets where the set $\alpha$-open sets are defined. Properties of this set and some relationships were presented, in addition to studying a set of functions, including open, closed and continuous functions, finding the relationship between them and giving examples and properties that belong to this set, which will be a starting point for studying many topological properties using this set.


[1] G. Choquet, Sur les notions de filtre et grille, Compt. Rend. Acad. Sci. Paris 224 (1947) 171–173.
[2] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer Math. Month. 70 (1963) 36–41.
[3] M.O. Mustafa and R.B. Esmaeel, Separation axioms with grill-toplogical open set, J. Phys. Conf. Ser. 1879(2)
(2021) 022107.
[4] M.O. Mustafa and R.B. Esmaeel, Some properties in grill-topological open and closed sets, J. Phys. Conf. Ser.
1897(1) (2021), 012038.
[5] A.I. Nasir and R.B. Esmaeel, On α-J-space On �-J-space, JARDCS 11(1) (2019) 1379–1382.
[6] B. Roy and M.N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math. 33(4) (2007) 771–786.
[7] S.G. Saeed and R.B. Esmaeel, Separation axioms via αg-open set, J. Phys. Conf. Ser. 1591(1) (2020) 012099.
[8] D. Saravanakumar and N. Kalaivani, On grill Sp-open set in grill topological spaces, J. New Theory 23 (2018)
Volume 13, Issue 1
March 2022
Pages 3765-3772
  • Receive Date: 12 December 2021
  • Revise Date: 07 January 2022
  • Accept Date: 03 February 2022
  • First Publish Date: 03 February 2022