CHARACTERIZATIONS OF γ- PS-REGULAR
AND γ- PS-NORMAL SPACES
Nazihah Ahmad1, Baravan A. Asaad2, Zurni Omar3
1,3School of Quantitative Sciences
College of Arts and Sciences
Universiti Utara Malaysia
06010 Sintok, Kedah, MALAYSIA
2 Department of Computer Science, College of Science
Cihan University-Duhok, IRAQ 2 Department of Mathematics, Faculty of Science
University of Zakho, IRAQ

Abstract

This paper defines some types of $\gamma$-$P_S$- separation axioms called $\gamma$-$P_S$-regular and $\gamma$-$P_S$-normal spaces using $\gamma$-$P_S$-open and $\gamma$-$P_S$-closed sets. Some relations, properties and characterizations of these spaces are discussed. Several examples are given to illustrate some of the results.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 4
Year: 2019

DOI: 10.12732/ijam.v32i4.5

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References

  1. [1] B.A. Asaad and N. Ahmad, Further characterization of -extremally disconnected spaces, International J. of Pure and Applied Mathematics, 108, No 3 (2016), 533-549.
  2. [2] B.A. Asaad, N. Ahmad and Z. Omar, -PS-functions in topological spaces, International J. of Mathematical Analysis, 8, No 6 (2014), 285-300.
  3. [3] B.A. Asaad, N. Ahmad and Z. Omar, -PS-generalized closed sets and PS-T1 2 spaces, International J. of Pure and Applied Mathematics, 93, No 2 (2014), 243-260.
  4. [4] B.A. Asaad, N. Ahmad and Z. Omar, -PS-open sets in topological spaces, Proc. of the 1st Innovation and Analytics Conference and Exhibition, UUM Press, Sintok (2013), 75-80.
  5. [5] B.A. Asaad, N. Ahmad and Z. Omar, ( , )-PS-irresolute and ( , )-PScontinuous functions, International J. of Pure and Applied Mathematics, 99, No 1 (2015), 77-96.
  6. [6] B.A. Asaad, N. Ahmad and Z. Omar, -regular-open sets and -extremally disconnected spaces, Mathematical Theory and Modeling, 3, No 12 (2013), 132-141.
  7. [7] B.A. Asaad, N. Ahmad and Z. Omar, Operation-separation axioms via -PS-open sets, International J. of Pure and Applied Mathematics, 118, No 3 (2018), 686-699.
  8. [8] M.K. Ghosh, On -preopen sets, International J. of Mathematical Analysis, 6, No 53 (2012), 2633-2645.
  9. [9] Sh. Haxha and Q.D. Gjonbalaj, ⋆-operation in the product of topological spaces, International J. of Applied Mathematics, 31, No 4 (2018), 661-672; DOI: 10.12732/ijam.v31i4.11.
  10. [10] D.S. Jankovic, On functions with -closed graphs, Glasnik Matematicki, 18, No 38 (1983), 141-148. 622 N. Ahmad, B.A. Asaad, Z. Omar
  11. [11] N. Kalaivani and G.S.S. Krishnan, On - -open sets in topological spaces, Proc. of ICMCM, 6 (2009), 370-376.
  12. [12] S. Kasahara, Operation compact spaces, Math. Japonica, 24, No 1 (1979), 97-105.
  13. [13] G.S.S. Krishnan and K. Balachandran, On a class of -preopen sets in a topological space, East Asian Math. J., 22, No 2 (2006), 131-149.
  14. [14] G.S.S. Krishnan and K. Balachandran, On -semiopen sets in topological spaces, Bull. Cal. Math. Soc., 98, No 6 (2006), 517-530.
  15. [15] H. Ogata, Operation on topological spaces and associated topology, Math. Japonica, 36, No 1 (1991), 175-184.
  16. [16] Z.A. Ameen, B.A. Asaad and R.A. Muhammed, On superclasses of -open sets in topological spaces, International J. of Applied Mathematics, 32, No 2 (2019), 259-277; DOI: 10.12732/ijam.v32i2.8.