On \(\theta(\tau_1,\tau_2)p\)-Open Functions and \(\theta(\tau_1,\tau_2)p\)-Closed Functions

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Napassanan Srisarakham, Areeyuth Sama-Ae, Chawalit Boonpok

Abstract

This paper deals with the concepts of \(\theta(\tau_1,\tau_2)p\)-open functions and \(\theta(\tau_1,\tau_2)p\)-closed functions. Moreover, several characterizations and some properties concerning \(\theta(\tau_1,\tau_2)p\)-open functions and \(\theta(\tau_1,\tau_2)p\)-closed functions are considered.

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References

  1. M.E. Abd El-Monsef, S.N. El-Deeb, R.A. Mahmoud, $beta$-Open Sets and $beta$-Continuous Mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
  2. C. Boonpok, P. Pue-on, Weakly $theta s(Lambda,p)$-open functions and weakly $theta s(Lambda,p)$-closed functions, Asia Pac. J. Math. 11 (2024), 13. https://doi.org/10.28924/APJM/11-13.
  3. C. Boonpok, M. Thongmoon, Weakly $p(Lambda,p)$-Open Functions and Weakly $p(Lambda,p)$-Closed Functions, Int. J. Ana. Appl. 22 (2024), 10. https://doi.org/10.28924/2291-8639-22-2024-10.
  4. C. Boonpok, M. Thongmoon, Properties of Weakly $beta(Lambda,p)$-Open Functions and Weakly $beta(Lambda,p)$-Closed Functions, Eur. J. Pure Appl. Math. 17 (2024), 248–255. https://doi.org/10.29020/nybg.ejpam.v17i1.4974.
  5. C. Boonpok, N. Srisarakham, $theta p(Lambda,p)$-Open Functions and $theta p(Lambda,p)$-Closed Functions, Asia Pac. J. Math. 10 (2023), 48. https://doi.org/10.28924/APJM/10-48.
  6. C. Boonpok, $(tau_1,tau_2)delta$-Semicontinuous Multifunctions, Heliyon, 6 (2020), e05367. https://doi.org/10.1016/j.heliyon.2020.e05367.
  7. C. Boonpok, C. Viriyapong, M. Thongmoon, on Upper and Lower $(tau_1,tau_2)$-Precontinuous Multifunctions, J. Math. Computer Sci. 18 (2018), 282–293. https://doi.org/10.22436/jmcs.018.03.04.
  8. C. Boonpok, Weakly Open Functions on Bigeneralized Topological Spaces, Int. J. Math. Anal. 4 (2010), 891–897.
  9. M. Caldas, S. Jafari, G. Navalagi, T. Noiri, On Pre-$theta$-Open Sets and Two Classes of Functions, Bull. Iran. Math. Soc. 32 (2006), 47–65.
  10. M. Caldas, G. Navalagi, On Weak Forms of Semi-Open and Semi-Closed Functions, Missouri J. Math. Sci. 18 (2006), 165–178.
  11. M. Caldas, G. Navalagi, On Weak Forms of Preopen and Preclosed Functions, Arch. Math. 40 (2004), 119–128. http://dml.cz/dmlcz/107896.
  12. M. Chiangpradit, S. Sompong, C. Boonpok, On Characterizations of $(tau_1,tau_2)$-Regular Spaces, Int. J. Math. Comput. Sci. 19 (2024), 1329–1334.
  13. N. Chutiman, C. Boonpok, Some Properties of Weakly $b(Lambda,p)$-Open Functions, Int. J. Math. Comput. Sci. 19 (2024), 497–501.
  14. J. Khampakdee, C. Boonpok, Properties of $(Lambda,p)$-Closed Functions, Int. J. Math. Comput. Sci. 19 (2024), 481–484.
  15. C. Klanarong, C. Boonpok, Characterizations of Weakly $delta(Lambda,p)$-Closed Functions, Int. J. Math. Comput. Sci. 19 (2024), 503–507.
  16. C. Klanarong, C. Boonpok, Characterizations of Weakly $s(Lambda,p)$-Open Functions and Weakly $s(Lambda,p)$-Closed Functions, Int. J. Math. Comput. Sci. 19 (2024), 809–814.
  17. A.S. Mashhour, I.A. Hasanein, S.N. El-Deeb, $alpha$-Continuous and $alpha$-Open Mappings, Acta Math. Hungar. 41 (1983), 213–218.
  18. A.S. Mashhour, M.E. Abd El-Monsef, S.N. El-Deeb, On Precontinuous and Weak Precontinuous Mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
  19. T. Noiri and V. Popa, A unified theory of closed functions, Bull. Math. Soc. Math. Roum. 49 (2006), 371–382.
  20. T. Noiri, On $theta$-Precontinuous Functions, Int. J. Math. Math. Sci. 28 (2001), 285–292. https://doi.org/10.1155/s0161171201006500.
  21. T. Noiri, A Generalization of Closed Mappings, Atti Acad. Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Nat. 54 (1973), 412–415. https://eudml.org/doc/293867.
  22. M.C. Pal, P. Bhattacharyya, Feeble and Strong Forms of Preirresolute Functions, Bull. Malays. Math. Soc. 19 (1996), 63–75.
  23. D.A. Rose, D.S. Jankovi'{c}, Weakly Closed Functions and Hausdorff Spaces, Math. Nachr. 130 (1987), 105–110.
  24. D.A. Rose, On Weak Openness and Almost Openness, Int. J. Math. Math. Sci. 7 (1984), 35–40.
  25. N. Srisarakham, C. Boonpok, On Weakly $delta(Lambda,p)$-Open Functions, Int. J. Math. Comput. Sci. 19 (2024), 485–489.
  26. N. Viriyapong, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Extremal Disconnectedness in Bitopological Spaces, Int. J. Math. Comput. Sci. 19 (2024), 855–860.
  27. C. Viriyapong, C. Boonpok, $(tau_1,tau_2)alpha$-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.