Characterizations of Almost \(\tau^\star(\sigma_1,\sigma_2)\)-Continuous Functions

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Napassanan Srisarakham, Areeyuth Sama-Ae, Chawalit Boonpok

Abstract

This paper deals with the concept of almost \(\tau^\star(\sigma_1,\sigma_2)\)-continuous functions. Moreover, several characterizations and some properties concerning almost \(\tau^\star(\sigma_1,\sigma_2)\)-continuous functions are investigated. Furthermore, the relationships between \(\tau^\star(\sigma_1,\sigma_2)\)-continuity and almost \(\tau^\star(\sigma_1,\sigma_2)\)-continuity are considered.

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References

  1. M.E. Abd El-Monsef, E.F. Lashien, A.A. Nasef, On $mathscr{I}$-Open Sets and $mathscr{I}$-Continuity, Kyungpook Math. J. 32 (1992), 21–30.
  2. 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.
  3. W. Al-Omeri, T. Noiri, On Almost $e$-$mathscr{I}$-Continuous Functions, Demonstr. Math. 54 (2021), 168–177. https://doi.org/10.1515/dema-2021-0014.
  4. D. Andrijevi'{c}, On $b$-Open Sets, Mat. Vesnik 48 (1996), 59–64.
  5. C. Boonpok, $pimath$-Continuity and Weak $pimath$-Continuity, Carpathian Math. Publ. 17 (2025), 171–186. https://doi.org/10.15330/cmp.17.1.171-186.
  6. C. Boonpok, P. Pue-On, Characterizations of Almost $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 22 (2024), 33. https://doi.org/10.28924/2291-8639-22-2024-33.
  7. C. Boonpok, C. Klanarong, On Weakly $(tau_1,tau_2)$-Continuous Functions, Eur. J. Pure Appl. Math. 17 (2024), 416–425. https://doi.org/10.29020/nybg.ejpam.v17i1.4976.
  8. C. Boonpok, P. Pue-on, Upper and Lower Weakly $alpha$-$star$-Continuous Multifunctions, Int. J. Anal. Appl. 21 (2023), 90. https://doi.org/10.28924/2291-8639-21-2023-90.
  9. C. Boonpok, N. Srisarakham, $(tau_1,tau_2)$-Continuity for Functions, Asia Pac. J. Math. 11 (2024), 21. https://doi.org/10.28924/APJM/11-21.
  10. C. Boonpok, on Some Spaces via Topological Ideals, Open Math. 21 (2023), 20230118. https://doi.org/10.1515/math-2023-0118.
  11. C. Boonpok, $theta(star)$-Precontinuity, Mathematica, 65 (2023), 31–42. https://doi.org/10.24193/mathcluj.2023.1.04.
  12. C. Boonpok, Weak Openness and Weak Continuity in Ideal Topological Spaces, Mathematica, 64 (2022), 173–185.
  13. C. Boonpok, $(tau_1,tau_2)delta$-Semicontinuous Multifunctions, Heliyon, 6 (2020), e05367. https://doi.org/10.1016/j.heliyon.2020.e05367.
  14. 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.
  15. M. Chiangpradit, S. Sompong, C. Boonpok, Weakly Quasi $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 22 (2024), 125. https://doi.org/10.28924/2291-8639-22-2024-125.
  16. E. Hatir and T. Noiri, On $beta$-$mathscr{I}$-Open Sets and a Decomposition of Almost $mathscr{I}$-Continuity, Bull. Malays. Math. Sci. Soc. 29 (2006), 119–124.
  17. D. Jankovic, T.R. Hamlet, New Topologies from Old via Ideals, Am. Math. Mon. 97 (1990), 295–310. https://doi.org/10.2307/2324512.
  18. A. Keskin, T. Noiri, Almost $b$-Continuous Functions, Chaos Solitons Fractals, 41 (2009), 72–81. https://doi.org/10.1016/j.chaos.2007.11.012.
  19. J. Khampakdee, A. Sama-Ae, C. Boonpok, Upper and Lower Continuous Multifunctions Defined Between an Ideal Topological Space and a Bitopological Space, Eur. J. Pure Appl. Math. 18 (2025), 6565. https://doi.org/10.29020/nybg.ejpam.v18i3.6565.
  20. B. Kong-ied, A. Sama-Ae, C. Boonpok, Almost Quasi $tau^star(sigma_1,sigma_2)$-Continuous and Weakly Quasi $tau^star(sigma_1,sigma_2)$-Continuous Functions, Eur. J. Pure Appl. Math. 18 (2025), 6572. https://doi.org/10.29020/nybg.ejpam.v18i3.6572.
  21. B. Kong-ied, S. Sompong, C. Boonpok, Almost Quasi $(tau_1,tau_2)$-Continuous Functions, Asia Pac. J. Math. 11 (2024), 64. https://doi.org/10.28924/APJM/11-64.
  22. K. Kuratowski, Topology, Academic Press, 1966.
  23. S.N. Maheshwari, G.I. Chae, P.C. Jain, Almost Feebly Continuous Functions, Ulsan Inst. Tech. Rep. 13 (1982), 195–197.
  24. S. Marcus, Sur les Fonctions Quasicontinues au Sens de S. Kempisty, Colloq. Math. 8 (1961), 47–53. https://eudml.org/doc/210887.
  25. 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.
  26. B.M. Munshi, D.S. Bassan, Almost Semi-Continuous Mappings, Math. Student, 49 (1981), 239–248.
  27. A.A. Nasef, T. Noiri, Some Weak Forms of Almost Continuity, Acta Math. Hungar. 74 (1997), 211–219.
  28. T. Noiri, V. Popa, On $(mI,nJ)$-Continuous Multifunctions, Rom. J. Math. Comput. Sci. 15 (2025), 1–8.
  29. T. Noiri, Almost $alpha$-Continuous Functions, Kyungpook Math. J. 28 (1988), 71–77.
  30. V. Popa, On a Decomposition of Quasicontinuity in Topological Spaces, Stud. Cerc. Mat. 30 (1978), 31–35.
  31. M.K. Singal, A.R. Singal, Almost Continuous Mappings, Yokohama J. Math. 16 (1968), 63–73.
  32. M. Thongmoon, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Continuous Multifunctions and $tau_1tau_2$-$delta$-Open Sets, Int. J. Math. Comput. Sci. 19 (2024), 1369–1375.
  33. N. Viriyapong, A. Sama-Ae, C. Boonpok, On Almost $tau^star(sigma_1,sigma_2)$-Continuity and Weak $tau^star(sigma_1,sigma_2)$-Continuity, Eur. J. Pure Appl. Math. 18 (2025), 6568. https://doi.org/10.29020/nybg.ejpam.v18i3.6568.
  34. N. Viriyapong, S. Sompong, C. Boonpok, Upper and Lower $s$-$(tau_1,tau_2)p$-Continuous Multifunctions, Eur. J. Pure Appl. Math. 17 (2024), 2210–2220. https://doi.org/10.29020/nybg.ejpam.v17i3.5322.
  35. N. Viriyapong, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Extremal Disconnectedness in Bitopological Spaces, Int. J. Math. Comput. Sci. 19 (2024), 855–860.
  36. C. Viriyapong, C. Boonpok, $(tau_1,tau_2)alpha$-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.
  37. S. Y"{u}ksel, A. Ac{c}ikg"{o}z, T. Noiri, On $delta$-$mathscr{I}$-Continuous Functions, Turk. J. Math. 29 (2005), 39–51.