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On minimal upper semicontinuous compact-valued maps. (English) Zbl 0742.54006
A compact-valued, usc multifunction \(F: X\to Y\) is called minimal, if it does not exist any compact-valued usc \(G: X\to Y\) such that \[ \emptyset \neq G(x) \subseteq F(x) \] for all \(x\in X\) and \(F\neq G\). Many interesting characterizations of such multifunctions are given using the cluster set technique.

54C60 Set-valued maps in general topology
26E25 Set-valued functions
54C08 Weak and generalized continuity
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