Micro Separation Axioms

Article Sidebar

PDF
Cite as:
Hariwan Z. Ibrahim, Micro Separation Axioms, Int. J. Anal. Appl., 18 (4) (2020), 572-585.

Main Article Content

Hariwan Z. Ibrahim

Abstract

In this paper, some new types of spaces are defined and studied in micro topological spaces namely, Micro T0, Micro T1, Micro T2, Micro R0 and Micro R1 spaces. Properties and the relationships of these spaces are introduced. Finally, the relationships between these spaces and the related concepts are investigated.

Article Details

References

  1. S. Chandrasekar, On micro topological spaces, J. New Theory, 26 (2019) 23-31.
  2. H. Z. Ibrahim, On new separation axioms via γ-open sets, Int. J. Adv. Res. Technol. 1 (1) (2012), 1-3.
  3. H. Z. Ibrahim, Operation on regular spaces, J. Adv. Stud. Topol. 4 (1) (2013), 138-149.
  4. H. Z. Ibrahim, Weak forms of γ-open sets and new separation axioms, Int. J. Sci. Eng. Res. 3 (4) (2012), 1-4.
  5. H. Z. Ibrahim, b-γ-continuous and b-γ-irresolute, Int. Electron. J. Pure Appl. Math. 5 (4) (2012), 145-156.
  6. H. Z. Ibrahim, α-γ-g.closed sets and α-γ-g.closed graph, Int. J. Pure Appl. Math. 83 (4) (2013), 575-588.
  7. H. Z. Ibrahim, Pre-γ-T 1 2 and pre-γ-continuous, J. Adv. Stud. Topol. 4 (2) (2013), 1-9.
  8. H. Z. Ibrahim, β-γ-irresolute and β-γ-closed graph, Gen. Math. Notes, 15 (2) (2013), 32-44.
  9. H. Z. Ibrahim, On some separation axioms via β-γ-open sets, Gen. Math. Notes, 15 (2) (2013), 14-31.
  10. H. Z. Ibrahim, On a class of αγ-open sets in a topological space, Acta Sci. Technol. 35 (3) (2013), 539-545.
  11. H. Z. Ibrahim, On a class of γ-b-open sets in a topological space, Gen. Math. Notes, 16 (2) (2013), 66-82.
  12. H. Z. Ibrahim, Bc-separation axioms in topological spaces, Gen. Math. Notes, 17 (1) (2013), 45-62.
  13. H. Z. Ibrahim, α γ-open sets, α γ-functions and some new separation axioms, Acta Sci. Technol. 35 (4) (2013), 725-731.
  14. H. Z. Ibrahim, On α(γ,γ 0 ) -separation axioms, Int. J. Anal. Appl. 16 (5) (2018), 775-782.
  15. H. Z. Ibrahim, On Micro b-open Sets, Communicated.
  16. H. Z. Ibrahim, On micro T 1 2 space, Int. J. Appl. Math. in press.
  17. A. B. Khalaf and and H. Z. Ibrahim, Some applications of γ-P-open sets in topological spaces, Int. J. Pure Appl. Math. Sci. 5 (1-2) (2011), 81-96.
  18. A. B. Khalaf and H. Z. Ibrahim, Pγ-open sets and Pγ,β-continuous mappings in topological spaces, J. Adv. Stud. Topol. 3 (4) (2012), 102-110.
  19. A. B. Khalaf, H. Z. Ibrahim and A. K. Kaymakci, Operation-separation axioms via α-open sets, Acta Univ. Apulensis, (47) (2016), 99-115.
  20. A. B. Khalaf, S. Jafari and H. Z. Ibrahim, Bioperations on α-separations axioms in topological spaces, Sci. Math. Jpn. 81 (2018), 1-15.
  21. A. M. Kozae, S. A. Saleh , M. A. Elsafty and M. M. Salama, Entropy measures for topological approximations of uncertain concepts, Jokull J. 65 (1) (2015), 192-206.
  22. Z. Pawlak, Rough sets, Int. J. Inform. Computer Sci. 11 (1982), 341-356.
  23. Z. Pawlak, Granularity of knowledge, indiscernibility and rough sets, Proc. IEEE Int. Conf. Fuzzy Syst. (1998), 106-110.
  24. I. L. Reilly and M. K. Vamanamurthy, On α-sets in topological spaces, Tamkang J. Math. 16 (1985), 7-11.
  25. M. L. Thivagar and C. Richard, Note on nano topological spaces, Communicated.
  26. M. L. Thivagar, C. Richard and N. R. Paul, Mathematical Innovations of a Modern Topology in Medical Events, Int. J. Inform. Sci. 2 (4) (2012), 33-36.