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Weak and strong forms of continuity of multifunctions. (English) Zbl 1132.54309

Summary: We introduce new forms of continuity of multifunctions by using the concepts of locally closed sets and clopen sets. Some properties of these multifunctions are studied and the relationships between several weak and strong forms of continuity of multifunctions are investigated.

MSC:

54C08 Weak and generalized continuity
54C60 Set-valued maps in general topology
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References:

[1] Baurbaki, N., General topology, Part I (1966), AdditionWesley Publ. Co.: AdditionWesley Publ. Co. Reading, Mass
[2] Njaslad, O., On some classes of nearly open sets, Pacific J Math, 15, 961-970 (1965) · Zbl 0137.41903
[3] Mashour, A. S.; El Monsef, Abd; El-Deep, S. N., On precontinuous mappings, Proc Math Phys Soc, Egypt, 51 (1981) · Zbl 0571.54011
[4] Levine, N., Strong continuity in topological spaces, Am Math Monthly, 67, 269 (1960) · Zbl 0156.43305
[5] Arya, S. P.; Gupta, R., On strongly continuous mappings, Kyungpook Math J, 14, 131-143 (1974) · Zbl 0328.54006
[6] Ganster, M.; Reilly, I. L., Locally closed sets and LC—Continuous functions, Int J Math Math Sci, 12, 3, 417-424 (1989) · Zbl 0676.54014
[7] Noiri, T.; Popa, V., On upper and lower \(α\)—Continuous multifunctions, Problemy Mat Slovaca, 43, 381-396 (1968) · Zbl 0899.54015
[8] Popa, V., Some properties of \(H\)—Almost continuous multifunctions, Problemy Mat Slovaca, 10, 9-26 (1988) · Zbl 0707.54014
[9] Dontchev, J., Contra continuous functions and strongly \(S\)—Closed spaces, Int J Math Math Sci, 19, 2, 303-310 (1996) · Zbl 0840.54015
[10] Singal, M. K.; Mathur, A., A note on mildly compact spaces, Kyungpook Math J, 9, 165-168 (1979) · Zbl 0439.54021
[11] El Naschie, Ms. G.; Rossler, Oe.; Oed, G., Information and diffusion in quantum physics, Chaos Solitons & Fractals, 5 (2004)
[12] El Naschie, Ms. G., “Quantum gravity”, Clifford algebra, fuzzy set theory and the fundamental constants of nature, Chaos, Solitons & Fractals, 20, 437-450 (2004) · Zbl 1054.83502
[13] El Naschie, Ms. G., The symplictic vacuum, exotic quasi-particles and gravitational instanton, Chaos, Solitons & Fractals, 22, 1-11 (2004) · Zbl 1066.83535
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