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Decompositions of continuity for multifunctions. (English) Zbl 1383.54017

Summary: Investigations of decompositions of continuity for functions between topological spaces has a large literature, but extension of this topic to multifunctions has not yet been investigated. The aim of the present note is to introduce the study of decompositions of continuity for multifunction.
For this purpose we will generalize the methods introduced by the author [Acta Math. Hung. 61, No. 1–2, 93–98 (1993; Zbl 0820.54006)] and later used by J. Dontchev and the author [Acta Math. Hung. 71, No. 1–2, 109–120 (1996; Zbl 0852.54012)] and in many papers including for example [E. Hatir and M. Caldas, Arab. J. Sci. Eng. (AJSE), Math. 35, No. 2D, 197–202 (2010; Zbl 1218.54012)] and [T. Noiri and V. Popa, Acta Math. Hung. 128, No. 1–2, 175–189 (2010; Zbl 1224.54006)].

MSC:

54C05 Continuous maps
54C08 Weak and generalized continuity
54C60 Set-valued maps in general topology
58C07 Continuity properties of mappings on manifolds
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