Weak (τ1, τ2)-Continuity for Multifunctions

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Napassanan Srisarakham, Supannee Sompong, Chawalit Boonpok


This paper is concerned with the concept of weakly (τ1, τ2)-continuous multifunctions. Moreover, several characterizations of weakly (τ1, τ2)-continuous multifunctions are investigated.

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  1. C. Berge, Espaces Topologiques Fonctions Multivoques, Dunod, Paris, 1959.
  2. C. Boonpok, C. Klanarong, On Weakly (τ1, τ2)-Continuous Functions, Eur. J. Pure Appl. Math. 17 (2024), 416–425. https://doi.org/10.29020/nybg.ejpam.v17i1.4976.
  3. C. Boonpok, Weak Openness and Weak Continuity in Ideal Topological Spaces, Mathematica 64 (2022), 173–185. https://doi.org/10.24193/mathcluj.2022.2.03.
  4. C. Boonpok, C. Viriyapong, Upper and Lower Almost Weak (τ1, τ2)-Continuity, Eur. J. Pure Appl. Math. 14 (2021), 1212–1225. https://doi.org/10.29020/nybg.ejpam.v14i4.4072.
  5. C. Boonpok, Upper and Lower β(*)-Continuity, Heliyon, 7 (2021), e05986. https://doi.org/10.1016/j.heliyon.2021.e05986.
  6. C. Boonpok, (τ1, τ2)δ-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 (τ1, τ2)-Precontinuous Multifunctions, J. Math. Computer Sci. 18 (2018), 282–293. https://doi.org/10.22436/jmcs.018.03.04.
  8. C. Boonpok, M-Continuous Functions in Biminimal Structure Spaces, Far East J. Math. Sci. 43 (2010), 41–58.
  9. E. Ekici, S. Jafari, M. Caldas, T. Noiri, Weakly λ-Continuous Functions, Novi Sad J. Math. 38 (2008), 47–56.
  10. K. Laprom, C. Boonpok, C. Viriyapong, β(τ1, τ2)-Continuous Multifunctions on Bitopological Spaces, J. Math. 2020 (2020), 4020971. https://doi.org/10.1155/2020/4020971.
  11. N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. Math. Mon. 70 (1963), 36–41. https://doi.org/10.1080/00029890.1963.11990039.
  12. N. Levine, A Decomposition of Continuity in Topological Spaces, Amer. Math. Mon. 68 (1961), 44–46. https://doi.org/10.2307/2311363.
  13. S. Marcus, Sur les Fonctions Quasicontinues au Sens de S. Kempisty, Colloq. Math. 8 (1961), 47–53.
  14. A. Neubrunnová, On Certain Generalizations of the Notions of Continuity, Mat. Casopis, 23 (1973), 374–380. http://dml.cz/dmlcz/126571.
  15. T. Noiri, Properties of Some Weak Forms of Continuity, Int. J. Math. Math. Sci. 10 (1987), 97–111. https://doi.org/10.1155/s0161171287000139.
  16. V. Popa, T. Noiri, On Weakly (τ, m)-Continuous Functions, Rend. Circ. Mat. Palermo 51 (2002), 295–316. https://doi.org/10.1007/bf02871656.
  17. V. Popa, T. Noiri, A Unified Theory of Weak Continuity for Functions, Rend. Circ. Mat. Palermo 51 (2002), 439–464. https://doi.org/10.1007/bf02871853.
  18. V. Popa, T. Noiri, On Some Weak Forms of Continuity for Multifunctions, Istanbul Üniv. Fen. Fak. Mat. Der. 60 (2001), 55–72.
  19. V. Popa, C. Stan, On a Decomposition of Quasicontinuity in Topological Spaces, Stud. Cerc. Mat. 25 (1973), 41–43.
  20. D.A. Rose, Weak Continuity and Almost Continuity, Int. J. Math. Math. Sci. 7 (1984), 311–318. https://doi.org/10.1155/S0161171284000338.
  21. C. Viriyapong, C. Boonpok, (τ1, τ2)α-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.