Borwein, J.; Kortezov, I. Constructive minimal uscos. (English) Zbl 1059.54019 C. R. Acad. Bulg. Sci. 57, No. 12, 9-12 (2004). 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. Reviewer: Angela Slavova (Sofia) Cited in 3 Documents MSC: 54C60 Set-valued maps in general topology Keywords:minimal usco; axiom of choice; constructibility PDFBibTeX XMLCite \textit{J. Borwein} and \textit{I. Kortezov}, C. R. Acad. Bulg. Sci. 57, No. 12, 9--12 (2004; Zbl 1059.54019)