ON MICRO $T_{1\over 2}$ SPACE

Abstract

The aim of this paper is to introduce and study different properties of Micro generalized closed set in micro topological space. As applications to Micro generalized closed set, we introduce Micro $T_{1\over 2}$ space and obtain some of their basic properties. We analyze the behavior of Micro generalized closed set and Micro $T_{1\over 2}$ space under Micro-continuous and Micro-closed functions. Also, we introduce the notions of Micro difference sets and Micro kernel of sets and investigate some of their fundamental properties.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 3
Year: 2020

DOI: 10.12732/ijam.v33i3.1

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] S. Chandrasekar, On micro topological spaces, Journal of New Theory, 26 (2019), 23-31.
  2. [2] H.Z. Ibrahim, γgb-closed sets in topological spaces, Journal of Advanced Studies in Topology, 4, No 1 (2013), 73-79.
  3. [3] H.Z. Ibrahim, γ-semi-open sets and γ-semi-functions, Journal of Advanced Studies in Topology, 4, No 1 (2013), 55-65.
  4. [4] H.Z. Ibrahim, On new separation axioms via γ-open sets, International Journal of Advancements in Research & Technology, 1, No 1 (2012), 1214.
  5. [5] H.Z. Ibrahim, Operation on regular spaces, Journal of Advanced Studies in Topology, 4, No 1 (2013), 138-149.
  6. [6] H.Z. Ibrahim, Weak forms of γ-open sets and new separation axioms, Int. J. of Scientific and Engineering Research, 3, No 4 (2012), 1-4.
  7. [7] H.Z. Ibrahim, b-γ-continuous and b-γ-irresolute, International Electronic Journal of Pure and Applied Mathematics, 5, No 4 (2012), 145-156.
  8. [8] H.Z. Ibrahim, α-γ-g.closed sets and α-γ-g.closed graph, International Journal of Pure and Applied Mathematics, 83, No 4 (2013), 575-588; doi: 10.12732/ijpam.v83i4.6.
  9. [9] H.Z. Ibrahim, Pre-γ-T1 2 and pre-γ-continuous, Journal of Advanced Studies in Topology, 4, No 2 (2013), 1-9.
  10. [10] H.Z. Ibrahim, -γ-irresolute and -γ-closed graph, Gen. Math. Notes, 15, No 2 (2013), 32-44.
  11. [11] H.Z. Ibrahim, On a class of αγ-open sets in a topological space, Acta Scientiarum. Technology, 35, No 3 (2013), 539-545; doi: 10.4025/actascitechnol.v35i3.15788.
  12. [12] H.Z. Ibrahim, On a class of γ-b-open sets in a topological space, Gen. Math. Notes, 16, No 2 (2013), 66-82.
  13. [13] H.Z. Ibrahim, Bc-separation axioms in topological spaces, Gen. Math. Notes, 17, No 1 (2013), 45-62.
  14. [14] H.Z. Ibrahim, αγ-open sets, αγ-functions and some new separation axioms, Acta Scientiarum. Technology, 35, No 4 (2013), 725-731; doi: 10.4025/actascitechnol.v35i4.15728.
  15. [15] H.Z. Ibrahim, Strong forms of generalized closed sets in ditopological texture spaces, Journal of Advanced Studies in Topology, 6, No 2 (2015), 61-68; doi: 10.20454/jast.2015.908.
  16. [16] H.Z. Ibrahim, On α(γ,γ′ )-open sets in topological spaces, New Trends in Mathematical Sciences, 6, No 2 (2018), 150-158; doi: 10.20852/ntmsci.2018.280.
  17. [17] H.Z. Ibrahim, On Micro b-open Sets, Submitted.
  18. [18] A.B. Khalaf and and H.Z. Ibrahim, Some applications of γ-P-open sets in topological spaces, International Journal of Pure and Applied Mathematical Sciences, 5, No 1-2 (2011), 81-96.
  19. [19] A.B. Khalaf and H.Z. Ibrahim, Pγ-open sets and Pγ, -continuous mappings in topological spaces, Journal of Advanced Studies in Topology, 3, No 4 (2012), 102-110.
  20. [20] A.B. Khalaf and H.Z. Ibrahim, On some separation axioms via -γ-open sets, Gen. Math. Notes, 15, No 2 (2013), 14-31.
  21. [21] A.B. Khalaf and H.Z. Ibrahim, Some properties of operations on αo(X), International Journal of Mathematics and Soft Computing, 6, No 1 (2016), 107-120.
  22. [22] A.B. Khalaf, S. Jafari and H.Z. Ibrahim, Bioperations on α-separations axioms in topological spaces, Scientiae Mathematicae Japonicae Online, Whole Number 29 (2016), 1-13.
  23. [23] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (1970), 89-96.
  24. [24] Z. Pawlak, Rough sets, International journal of information and computer sciences, 11 (1982), 341-356.
  25. [25] I.L. Reilly and M.K. Vamanamurthy, On α-sets in topological spaces, Tamkang J. Math., 16 (1985), 7-11.
  26. [26] M.L. Thivagar and C. Richard, Note on nano topological spaces, Communicated.
  27. [27] M.L. Thivagar, C. Richard and N.R. Paul, Mathematical innovations of a modern topology in medical events, International Journal of Information Science, 2, No 4 (2012), 33-36; doi: 10.5923/j.ijis.20120204.01.