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Constructive minimal uscos. (English) Zbl 1059.54019

In this paper a minimal usco mapping contained in a given usco with finite-dimensional target is explicitly constructed. A map (set-valued) \( F:Z \rightarrow X \) is called an usco, if it is upper semicontinuous and \( F(z) \) is a nonempty compact set for every \( z \in Z \). The authors prove that in the general case the existence of such a minimal usco is equivalent to Axiom of Choice.

MSC:

54C60 Set-valued maps in general topology
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