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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.

##### MSC:
 54C60 Set-valued maps in general topology 26E25 Set-valued functions 54C08 Weak and generalized continuity
##### Keywords:
upper semicontinuity; minimal maps; multifunction; cluster set
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##### References:
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