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

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.

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References


  1. S. Chandrasekar, On micro topological spaces, J. New Theory, 26 (2019) 23-31. Google Scholar

  2. H. Z. Ibrahim, On new separation axioms via γ-open sets, Int. J. Adv. Res. Technol. 1 (1) (2012), 1-3. Google Scholar

  3. H. Z. Ibrahim, Operation on regular spaces, J. Adv. Stud. Topol. 4 (1) (2013), 138-149. Google Scholar

  4. H. Z. Ibrahim, Weak forms of γ-open sets and new separation axioms, Int. J. Sci. Eng. Res. 3 (4) (2012), 1-4. Google Scholar

  5. H. Z. Ibrahim, b-γ-continuous and b-γ-irresolute, Int. Electron. J. Pure Appl. Math. 5 (4) (2012), 145-156. Google Scholar

  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. Google Scholar

  7. H. Z. Ibrahim, Pre-γ-T 1 2 and pre-γ-continuous, J. Adv. Stud. Topol. 4 (2) (2013), 1-9. Google Scholar

  8. H. Z. Ibrahim, β-γ-irresolute and β-γ-closed graph, Gen. Math. Notes, 15 (2) (2013), 32-44. Google Scholar

  9. H. Z. Ibrahim, On some separation axioms via β-γ-open sets, Gen. Math. Notes, 15 (2) (2013), 14-31. Google Scholar

  10. H. Z. Ibrahim, On a class of αγ-open sets in a topological space, Acta Sci. Technol. 35 (3) (2013), 539-545. Google Scholar

  11. H. Z. Ibrahim, On a class of γ-b-open sets in a topological space, Gen. Math. Notes, 16 (2) (2013), 66-82. Google Scholar

  12. H. Z. Ibrahim, Bc-separation axioms in topological spaces, Gen. Math. Notes, 17 (1) (2013), 45-62. Google Scholar

  13. H. Z. Ibrahim, α γ-open sets, α γ-functions and some new separation axioms, Acta Sci. Technol. 35 (4) (2013), 725-731. Google Scholar

  14. H. Z. Ibrahim, On α(γ,γ 0 ) -separation axioms, Int. J. Anal. Appl. 16 (5) (2018), 775-782. Google Scholar

  15. H. Z. Ibrahim, On Micro b-open Sets, Communicated. Google Scholar

  16. H. Z. Ibrahim, On micro T 1 2 space, Int. J. Appl. Math. in press. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  22. Z. Pawlak, Rough sets, Int. J. Inform. Computer Sci. 11 (1982), 341-356. Google Scholar

  23. Z. Pawlak, Granularity of knowledge, indiscernibility and rough sets, Proc. IEEE Int. Conf. Fuzzy Syst. (1998), 106-110. Google Scholar

  24. I. L. Reilly and M. K. Vamanamurthy, On α-sets in topological spaces, Tamkang J. Math. 16 (1985), 7-11. Google Scholar

  25. M. L. Thivagar and C. Richard, Note on nano topological spaces, Communicated. Google Scholar

  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. Google Scholar


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