A Unified Theory of Near Continuity for Functions Defined Between an Ideal Topological Space and a Bitopological Space

Main Article Content

Butsakorn Kong-ied, Areeyuth Sama-Ae, Chawalit Boonpok

Abstract

This paper introduces a new class of continuous functions defined from an ideal topological space into a bitopological space, namely nearly \(\tau^\star(\sigma_1,\sigma_2)\)-continuous functions. Furthermore, several characterizations and some properties concerning nearly \(\tau^\star(\sigma_1,\sigma_2)\)-continuous functions are investigated.

Article Details

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. 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.
  3. 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.
  4. 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.
  5. 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.
  6. C. Boonpok, on Some Spaces via Topological Ideals, Open Math. 21 (2023), 20230118. https://doi.org/10.1515/math-2023-0118.
  7. C. Boonpok, $theta(star)$-Precontinuity, Mathematica, 65 (2023), 31–42. https://doi.org/10.24193/mathcluj.2023.1.04.
  8. C. Boonpok, Weak Openness and Weak Continuity in Ideal Topological Spaces, Mathematica, 64 (2022), 173–185.
  9. C. Boonpok, $(tau_1,tau_2)delta$-Semicontinuous Multifunctions, Heliyon, 6 (2020), e05367. https://doi.org/10.1016/j.heliyon.2020.e05367.
  10. 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.
  11. D. Carnahan, Locally Nearly Compact Spaces, Boll. Un. Mat. Ital. (4), 6 (1972), 143–153.
  12. N. Chutiman, A. Sama-Ae, C. Boonpok, Almost Near $(tau_1,tau_2)$-Continuity for Multifunctions, Eur. J. Pure Appl. Math. 18 (2025), 5650. https://doi.org/10.29020/nybg.ejpam.v18i1.5650.
  13. N. Chutiman, S. Sompong, C. Boonpok, Characterizations of Nearly $(tau_1,tau_2)$-Continuous Functions, Asia Pac. J. Math. 12 (2025), 27. https://doi.org/10.28924/APJM/12-27.
  14. 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.
  15. M. Chiangpradit, S. Sompong, C. Boonpok, On Characterizations of $(tau_1,tau_2)$-Regular Spaces, Int. J. Math. Comput. Sci. 19 (2024), 1329–1334.
  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. E. Hatir, T. Noiri, On Decompositions of Continuity via Idealization, Acta Math. Hung. 96 (2002), 341–349. https://doi.org/10.1023/A:1019760901169.
  18. D. Jankovic, T.R. Hamlet, New Topologies from Old via Ideals, Am. Math. Mon. 97 (1990), 295–310. https://doi.org/10.2307/2324512.
  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 and C. Boonpok, Almost Nearly $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 23 (2025), 14. https://doi.org/10.28924/2291-8639-23-2025-14.
  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, Vol. I, Academic Press, New York, 1966.
  23. S.R. Malghan, V.V. Hanchinamani, $mathrm{N}$-Continuous Functions, Ann. Soc. Sci. Bruxelles, 98 (1984), 69–79.
  24. T. Noiri, V. Popa, On $(mI,nJ)$-Continuous Multifunctions, Rom. J. Math. Comput. Sci. 15 (2025), 1–8.
  25. T. Noiri, N. Ergun, Notes on $mathrm{N}$-Continuous Functions, Res. Rep. Yatsushiro Coll. Tech. 11 (1989), 65–68.
  26. T. Noiri, $mathrm{N}$-Closed Sets and Some Separation Axioms, Ann. Soc. Sci. Bruxelles, 88 (1974), 195–199.
  27. M. Thongmoon, A. Sama-Ae, C. Boonpok, Upper and Lower Near $(tau_1,tau_2)$-Continuity, Eur. J. Pure Appl. Math. 18 (2025), 5633. https://doi.org/10.29020/nybg.ejpam.v18i1.5633.
  28. 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.
  29. N. Viriyapong, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Extremal Disconnectedness in Bitopological Spaces, Int. J. Math. Comput. Sci. 19 (2024), 855–860.
  30. C. Viriyapong, C. Boonpok, $(tau_1,tau_2)alpha$-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.