ec55e7bf-b76d-4f1d-98be-872f5cc823f620210107041353045wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185Continuity for Multifunctions in Ideal Topological SpacesChawalitBoonpokMathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham, 44150, ThailandPrapartPue-OnMathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham, 44150, ThailandThis article presents the concept of ı ⋆ -continuous multifunctions in ideal topological spaces. Especially, several characterizations of ı ⋆ -continuous multifunctions are investigated. Moreover, the relationships between ı ⋆ -continuity and the other types of continuity for multifunctions are established.172021172021624631https://www.wseas.org/multimedia/journals/mathematics/2020/b405106-1224.pdf10.37394/23206.2020.19.69https://www.wseas.org/multimedia/journals/mathematics/2020/b405106-1224.pdfM.–E. Abd El-Monsef, E.–F. Lashien and A.– A. Nasef, On I -open sets and I -continuous functions, Kyungpook Math. J. 32, 1992, pp. 21– 30. A. Ac¸ikgoz, T. Noiri and S¸. Y ¨ uksel, A de- ¨ composition of continuity in ideal topological spaces, Acta Math. Hungar. 105, 2004, pp. 27– 37. C. Berge, Espaces topologiques fonctions multivoques, Dunod, Paris, 1959. 10.37418/amsj.9.1.28C. Boonpok, Weak quasi continuity for multifunctions in ideal topological spaces, Adv. Math., Sci. J. 9(1), 2020, pp. 339–355. 10.1134/s1995080219010049C. Boonpok, On continuous multifunctions in ideal topological spaces, Lobachevskii J. Math. 40, 2019, pp. 24–35. J. Dontchev, Idealization of Granter-Reilly decomposition theorems, arxiv:math. GN/9901017v1, 1999. 10.1007/bf02020262G. Freud, Ein Beitrag zu dem Satze von Cantor und Bendixson, Acta Math. Acad. Sci. Hungar. 9, 1958, pp. 333–336. 10.1007/s10474-005-0210-2E. Hatir, A. Keskin and T. Noiri, A note on strong β-I -open sets and strongly β-I - continuous functions, Acta Math. Hungar. 108, 2005, pp. 87–94. 10.1007/s10474-005-0202-2E. Hatir and T. Noiri, On semi-I -open sets and semi-I -continuous functions, Acta Math. Hungar. 107, 2005, pp. 345–353. E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar. 96, 2002, pp. 341–349. 10.1080/00029890.1990.11995593D. Jankovic and T.–R. Hamlett, New topologies ´ from old via ideals, Amer. Math. Monthly 97, 1990, pp. 295–310. K. Kuratowski, Topology, Vol. I, Academic– Press, New York, 1966. N. Levine, A Decomposition of continuity in topological spaces, Amer. Math. Monthly 68, 1961, pp. 44–46. T. Noiri and V. Popa, Weakly quasi-continuous multifunctions, Anal. Univ. Timis¸oara, Ser. Mat. 26, 1988, pp. 33–38. V. Popa and T. Noiri, Properties of weakly precontinuous multifunctions, Istanbul Univ. Fen. Fa. Mat. Dergisi 57/58, 1998/1999, pp. 41–52. V. Popa and T. Noiri, On weakly β-continuous multifunctions, Bui. St. Univ. ”Politehnica”, Sre. Mat. Fiz. Timis¸oara 45, 2000, pp. 1–16. D.–A. Rose, Weak continuity and almost continuity, Internat. J. Math. Math. Sci. 7, 1984, pp. 311–318. 10.1016/s0001-8708(71)80004-xS. Scheinberg, Topologies which generate a complete measure algebra, Advances in Math. 7, 1971, pp. 231–239. R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci. 20, 1944, pp. 51–61.