Operation on Generalized Semi Open Sets in Bitopological Spaces

Main Article Content

F. H. Khedr, M. Azab. Abd-Allah, E. A. Abdelgaber

Abstract

The aim of this paper is to more contribute the study of operations on bitopological spaces. The concept of operation on generalized semi open sets in bitopological spaces is introduced and studied. Two closure operators related to this concept are introduced and some of their properties and the relation between them are discussed.

Article Details

References

  1. M.E. Abd El-Monsef, A.M. Kozae, B.M. Taher, Compactification in Bitopological Spaces, Arab J. Sci. Eng. 22 (1997), 99–105.
  2. N. Ahmad, B.A. Asaad, More Properties of an Operation on Semi-Generalized Open Sets, Italian J. Pure Appl. Math. 39 (2018), 608–627
  3. T.V. An, D.X. Cuong, H. Maki, On Operation-Preopen Sets in Topological Spaces, Sci. Math. Japon. e-2008 (2008), 241–260.
  4. B.A. Asaad, Some Applications of Generalized Open Sets via Operations, New Trends Math. Sci. 1 (2017), 145–157. https://doi.org/10.20852/ntmsci.2017.132.
  5. B.A. Asaad, N. Ahmad, Operation on Semi Generalized Open Sets With Its Separation Axioms, Int. J. Pure Appl. Math. 118 (2018), 701–711.
  6. B.A. Asaad, Z.A. Ameen, Some Properties of an Operation on gα-Open Sets, New Trends Math. Sci. 2 (2019), 150–158. https://doi.org/10.20852/ntmsci.2019.353.
  7. S. Bose, Semi Open Sets, Semi Continuity and Semi Open Mappings in Bitopological Spaces, Bull. Calcutta Math. Soc. 73 (1981), 237–246.
  8. E. Rosas, C. Carpintero, N. Rajesh, Operation Approaches on b-Open Sets and Applications, Bol. Soc. Paran. Mat. 30 (2012), 21–33. https://doi.org/10.5269/bspm.v30i1.13013.
  9. D.S. Jankovic, On Functions with α-Closed Graphs, Glas. Mat. 18 (1983), 141–148.
  10. R. Jayashree, Operation Approach of gs-Open Sets in Topological Spaces, Thesis, Avinashilingam Deemed University for Women, 2019. http://hdl.handle.net/10603/302913.
  11. S. Kasahara, Operation-Compact Spaces, Math. Japon. 24 (1979), 97–105. https://cir.nii.ac.jp/crid/1572261549591870720.
  12. F.H. Khedr, Operation on Bitopologies, Delta J. Sci. 8 (1984), 309–320.
  13. F.H. Khedr, K.M. Abdelhakiem, Operations on Bitopological Spaces, Fasc. Math. 45 (2010), 47–57.
  14. F. Khedr, H. Al-Saadi, On Pairwise Semi-Generalized Closed Sets, J. King Abdulaziz Univ.: Sci. 21 (2009), 269–295. https://doi.org/10.4197/sci.21-2.7.
  15. F.H. Khedr, O.R. Sayed, Operation Pc-Open Sets and Operation Pc-Separation Axioms in Bitopological Spaces, Tatra Mount. Math. Publ. 85 (2023), 101–120. https://doi.org/10.2478/tmmp-2023-0027.
  16. G.S.S. Krishnan, Operation Approaches on Semi-Open Sets and Applications, Kochi J. Math. 2 (2007), 21–33.
  17. H. Ogata, Operations on Topological Spaces and Associated Topology, Math. Japon. 36 (1991), 175–184.
  18. S. Tahiliani, Operation Approach to β-Open Sets and Applications, Math. Comm. 16 (2011), 577–591.