Almost α-*-Continuity for Multifunctions

Main Article Content

Chawalit Boonpok, Napassanan Srisarakham

Abstract

This paper is concerned with the concepts of upper and lower almost α-*-continuous multifunctions. Moreover, several characterizations of upper and lower almost α-*-continuous multifunctions are investigated. In particular, the relationships between α-*-continuity and almost α-*-continuity are established.

Article Details

References

  1. M.E. Abd El-Monsef, E.F. Lashien, A.A. Nasef, On I -Open Sets and I - Continuous Functions, Kyungpook Math. J. 32 (1992), 21–30.
  2. A. Açıkgöz, T. Noiri, Ş. Yüksel, On *-Operfect Sets and α-*-Closed Sets, Acta Math Hung. 127 (2010), 146–153. https://doi.org/10.1007/s10474-010-9107-9.
  3. A. Açıkgöz, T. Noiri, Ş. Yüksel, On α-I-Continuous and α-I-Open Functions, Acta Math. Hung. 105 (2004), 27–37. https://doi.org/10.1023/b:amhu.0000045530.79591.d5.
  4. C. Berge, Espaces Topologiques Fonctions Multivoques, Dunod, Paris, 1959.
  5. C. Boonpok, J. Khampakdee, Upper and Lower α-*-Continuity, (accepted).
  6. C. Boonpok, Upper and Lower β(*)-Continuity, Heliyon, 7 (2021), e05986. https://doi.org/10.1016/j.heliyon.2021.e05986.
  7. C. Boonpok, On Some Types of Continuity for Multifunctions in Ideal Topological Spaces, Adv. Math., Sci. J. 9 (2020), 859–886.
  8. C. Boonpok, On Continuous Multifunctions in Ideal Topological Spaces, Lobachevskii J. Math. 40 (2019), 24–35. https://doi.org/10.1134/s1995080219010049.
  9. C. Boonpok, C. Viriyapong, M. Thongmoon, On Upper and Lower (τ1, τ2)-Precontinuous Multifunctions, J. Math. Computer Sci. 18 (2018), 282–293.
  10. E. Ekici, T. Noiri, *-hyperconnected ideal topological spaces, Ann. Alexandru Ioan Cuza Univ. - Math. 58 (2012), 121–129. https://doi.org/10.2478/v10157-011-0045-9.
  11. E. Ekici, On ACI -Sets, BCI -Sets, β*I -Open Sets and dEcompositions of Continuity in Ideal Topological Spaces, Creat. Math. Inform. 20 (2011), 47–54.
  12. E. Ekici, T. Noiri, *-Extremally Disconnected Ideal Topological Spaces, Acta Math. Hung. 122 (2008), 81–90. https://doi.org/10.1007/s10474-008-7235-2.
  13. E. Hatir, A. Keskin, T. Noiri, A Note on Strong β-I-Sets and Strongly β-I-Continuous Functions, Acta Math. Hung. 108 (2005), 87–94. https://doi.org/10.1007/s10474-005-0210-2.
  14. E. Hatir, T. Noiri, On Semi-I-Open Sets and Semi-I-Continuous Functions, Acta Math. Hung. 107 (2005), 345–353. https://doi.org/10.1007/s10474-005-0202-2.
  15. E. Hatir, A. Keskin, T. Noiri, On a New Decomposition of Continuity via Idealization, JP J. Geom. Topol. 3 (2003), 53–64.
  16. E. Hatir, T. Noiri, On Decompositions of Continuity via Idealization, Acta Math. Hung. 96 (2002), 341–349. https://doi.org/10.1023/a:1019760901169.
  17. D. Janković, T.R. Hamlett, New Topologies from Old via Ideals, Amer. Math. Mon. 97 (1990), 295–310. https://doi.org/10.1080/00029890.1990.11995593.
  18. K. Kuratowski, Topology, Vol. I, Academic Press, New York, 1966.
  19. O. Njåstad, On Some Classes of Nearly Open Sets, Pac. J. Math. 15 (1965), 961–970. https://doi.org/10.2140/pjm.1965.15.961.
  20. T. Noiri, Almost α-Continuous Functions, Kyungpook Math. J. 28 (1988), 71–77.
  21. V. Popa, T. Noiri, On Upper and Lower Almost α-Continuous Multifunctions, Demonstr. Math. 29 (1996), 381– 396. https://doi.org/10.1515/dema-1996-0215.
  22. V. Popa, T. Noiri, On Upper and Lower α-Continuous Multifunctions, Math. Slovaca, 43 (1993), 477–491. http://dml.cz/dmlcz/129754.
  23. V. Popa, Some Properties Of Almost Feebly Continuous Functions, Demonstr. Math. 23 (1990), 985–991. https://doi.org/10.1515/dema-1990-0415.
  24. V. Vaidyanathaswamy, The Localization Theory in Set Topology, Proc. Indian Acad. Sci. 20 (1945), 51–61.
  25. C. Viriyapong, C. Boonpok, (τ1, τ2)α-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.