References

  1. Abd El-Monsef M.E., Lashien E.F., Nasef A.A. On \(\mathscr{I}\)-open sets and \(\mathscr{I}\)-continuous functions. Kyungpook Math. J. 1992, 32 (1), 21–30.
  2. Abd El-Monsef M.E., El-Deeb S.N., Mahmoud R.A. \(\beta\)-open sets and \(\beta\)-continuous mappings. Bull. Fac. Sci. Assiut Univ. 1983, 12, 77–90.
  3. Açikgöz A., Noiri T., Yüksel Ş. A decomposition of continuity in ideal topological spaces. Acta Math. Hungar. 2004, 105, 285–289. doi:10.1023/B:AMHU.0000049280.10577.4e
  4. Al-Omeri W., Noiri T. On almost \(e\)-\(\mathscr{I}\)-continuous functions. Demonstr. Math. 2021, 54 (1), 168–177. doi:10.1515/dema-2021-0014
  5. Al-Omeri W. On mixed \(b\)-fuzzy topological spaces. Int. J. Fuzzy Log. Intell. Syst. 2020, 20 (3), 242–246. doi:10.5391/IJFIS.2020.20.3.242
  6. Al-Omeri W., Khalil O. H., Ghareeb A. Degree of \((L,M)\)-fuzzy semi-precontinuous and \((L,M)\)-fuzzy semi-preirresolute functions. Demonstr. Math. 2018, 51 (1), 182–197. doi:10.1515/dema-2018-0014
  7. Al-Omeri W., Noorani M.S.Md., Al-Omari A., Noiri T. New types of multifunctions in ideal topological spaces via \(e\)-\(\mathscr{I}\)-open sets and \(\delta\beta\)-\(\mathscr{I}\)-open sets. Bol. Soc. Parana. Mat. (3) 2016, 34 (1), 213–223. doi:10.5269/bspm.v34i1.26193
  8. Al-Omeri W., Noorani M.S.Md., Al-Omari A. On \(e\)-\(\mathscr{I}\)-open sets, \(e\)-\(\mathscr{I}\)-continuous functions and decomposition of continuity. J. Math. Appl. 2015, 38, 15–31. doi:10.7862/rf.2015.2
  9. Al-Omeri W., Noorani M.S.Md., Al-Omari A. New forms of contra-continuity in ideal topological spaces. Missouri J. Math. Sci. 2014, 26 (1), 33–47. doi:10.35834/mjms/1404997107
  10. Berge C. Espaces topologiques. Fonctions multivoques. Dunod., Paris, 1959.
  11. Boonpok C. On some types of continuity for multifunctions in ideal topological spaces. Adv. Math. Sci. 2020, 9 (3), 859–886. doi:10.37418/amsj.9.3.13
  12. Boonpok C. Weak quasi continuity for multifunctions in ideal topological spaces. Adv. Math. Sci. 2020, 9 (1), 339–355. doi:10.37418/amsj.9.1.28
  13. Boonpok C. On continuous multifunctions in ideal topological spaces. Lobachevskii J. Math. 2019, 40 (1), 24–35. doi:10.1134/S1995080219010049
  14. Dontchev J. Idealization of Ganster-Reilly decomposition theorems. arXiv:math/9901017 [math.GN]. doi:10.48550/arXiv.math/9901017
  15. Ekici E., Noiri T. \(\star\)-hyperconnected ideal topological spaces. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 2012, 58, 121–129. doi:10.2478/v10157-011-0045-9
  16. Hatir E., Keskin A., Noiri T. A note on strong \(\beta\)-\(\mathscr{I}\)-open sets and strongly \(\beta\)-\(\mathscr{I}\)-continuous functions. Acta Math. Hungar. 2005, 108 (1–2), 87–94. doi:10.1007/s10474-005-0210-2
  17. Hatir E., Noiri T. On semi-\(\mathscr{I}\)-open sets and semi-\(\mathscr{I}\)-continuous functions. Ata Math. Hungar. 2005, 107 (4), 345–353. doi:10.1007/s10474-005-0202-2
  18. Hatir E., Noiri T. On decompositions of continuity via idealization. Acta Math. Hungar. 2002, 96 (4), 341–349. doi:10.1023/A:1019760901169
  19. Husain T. Almost continuous mappings. Comment. Math. 1966, 10 (1), 1–7.
  20. Janković D., Hamlett T.R. New topologies from old via ideals. Amer. Math. Monthly 1990, 97, 295–310.
  21. Kuratowski K. Topology. Vol. I. Academic Press, INC. New York, 1966.
  22. Levine N. Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly 1963, 70, 36–41. doi:10.1080/00029890.1963.11990039
  23. Mashhour A.S., Abd El-Monsef M.E., El-Deeb S.N. On precontinuous and weak precontinuous mappings. Proc. Math. Phys. Soc. Egypt 1982, 53, 47–53.
  24. Njåstad O. On some classes of nearly open sets. Pacific J. Math. 1965, 15 (3), 961–970.
  25. Popa V., Noiri T. Properties of weakly precontinuous multifunctions. Istanb. Univ. Sci. Fac. J. Math. Phys. Astronom. 2001, 57-58, 41–52.
  26. Popa V., Noiri T. A note on precontinuity and quasicontinuity for multifunctions. Demonstr. Math. 1997, 30, 271–278.
  27. Popa V., Noiri T. Characterizations of \(\alpha\)-continuous multifunctions. Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 1993, 23 (1), 29–38.
  28. Przemski M. Some generalizations of continuity and quasicontinuity for multivalued maps. Demonstr. Math. 1993, 26 (2), 381–400. doi:10.1515/dema-1993-0212
  29. Vaidyanathaswamy R. The localisation theory in set topology. Proc. Indian Acad. Sci. Math. Sci. 1945, 20, 51–61. doi:10.1007/BF03048958
  30. Yüksel Ş., Simsekler T.H., Guzel Z., Noiri T. Strongly \(\theta\)-pre-\(\mathscr{I}\)-continuous functions. Sci. Stud. Res. Ser. Math. Inform. 2010, 20, 111–126.
  31. Yüksel Ş., Açikgöz A., Gursel E. On a new type of continuous functions in ideal topological spaces. J. Indian Math. Soc. (N.S.) 2007, 28, 427–438.
  32. Yüksel Ş., Açikgöz A., Gursel E. On \(\beta\)-\(\mathscr{I}\)-regular sets. Dal’nevost. Mat. Zh. 2007, 25, 353–366.
  33. Yüksel Ş., Açikgöz A., Noiri T. On \(\delta\)-\(\mathscr{I}\)-continuous functions. Turkish J. Math. 2005, 29 (1), 39–51.