New types of multifunctions in ideal topological spaces via $e$-$\I$-Open sets and $\delta\beta$-$\I$-Open sets
Abstract
The purpose of the present paper is to introduce and investigate two new classes of continuous multifunctions called upper/lower $e$-$\I$-continuous multifunctions and upper/lower $\delta\beta_I$-continuous multifunctions by using the concepts of $e$-$\I$-open sets and $\delta\beta_I$-open sets. The class of upper/lower $e$-$\I$-continuous multifunctions is contained in that of upper/lower $\delta\beta_I$-continuous multifunctions. Several characterizations and fundamental properties concerning upper/lower $e$-$\I$-continuity and upper/lower $\delta\beta_I$-continuity are obtained.
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References
M.E. Abd El-Monsef and A. A. Nasef, On Multifunctions, Chaos,Soliton and Fractals, 12 (2001), 2387-2394.
F. G. Arenas, J. Dontchev and M. L. Puertas, Idealization of some weak separation axioms, Acta Math. Hungar., 89 (1-2) (2000), 47- 53.
Al-Omeri W., Noorani M. S. M. & Al-Omari A. 2015. ON e-I-open sets, e-I-continuous functions and decomposition of continuity. J. Math. Appl.. No 38, pp (15-31).
W. Al-Omeri, M. Noorani and A. Al-Omari, New forms of contra-continuity in ideal topology spaces, Missouri J. Math. Sci., 26 (1) (2014), 33-47.
T. Banzaru, On the upper semicontiuity of upper topological limit for multifunction nets, Semin. Mat. Fiz. Inst. Politeh. "Tnaian Vuia" Timisoara, (1983), 59-64.
J. Dontchev, Strong B-sets and another decomposition of continuity, Acta Math. Hungar., 75 (1997), 259-265.
E. Ekici, On e-open sets, DP-sets and DPE-sets and decompositions of continuity, Arabian J. Sci. Eng. Vol 33, Number 2A (2008), 269-282.
E. Ekici, On e-open sets and (D, S)-sets, Math. Moravica, 13(1)(2009), 29û36.
E. Hatir, on decompositions of continuity and complete continuity in ideal topological spaces, Eur.J. Pure Appl. Math. 6(3)(2013), 352-362.
E. Hatir, A note on -I-open sets and semi-I-open sets, Math. Commun. 16(2011), 433-445.
D. Jankovic, T. R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295 - 310.
K. Kuratowski, Topology, Vol. I. New York: Academic Press (1966).
N. Levine, Semi-open sets and semi-continuity in topolological spaces, Amer. Math. Monthly, 70 (1963), 36-41.
M. N. Mukherjee, R. Bishwambhar and R. Sen, On extension of topological spaces in terms of ideals, Topology and its Appl., 154 (2007), 3167-3172.
A.S. Mashhour, M. E. Abd El-Monsef and S.N. El-Deeb, On pre-continuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53 (1982), 47-53.
J. H. Park, B. Y. Lee and M. J. Son, On -semiopen sets in topological space, J. Indian Acad. Math., 19 (1) (1997), 59-67.
T. Noiri and V. Popa, Almost weakly continuous multifunctions, Demonstratio Math., 26 (1993), 363-380.
S. Raychaudhuri and M.N. Mukherjee, On -almost continuity and -preopen sets, Bull. Inst. Math. Acad.Sinica, 21 (1993), 357-366.
A. A. Nasef and R. A. Mahmoud, Some applications via fuzzy ideals, Chaos, Solitons and Fractals, 13 (2002), 825 - 831.
A. A. Nithya and I. Arockiarani, Almost -pre-I-continuous multifunctions, Int. J. Contemp. Math. Sci., Vol. 5, (2010), no. 52, 2587-2594.
M.H. Stone, Application of the theory of boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375-481.
R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company (1960).
N.V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl.(2), 78(1968), 103-118.
R. Vaidyanathaswamy, The localization theory in set-topology, Proc. Indian Acad. Sci., 20 (1945), 51-61
S. Yüksel, A. Açikgöz and T. Noiri, On -I-continuous functions, Turk. J. Math., 29(2005), 39-51.
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