Geodesic
On a question of E.A. Michael
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 735-737

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A negative answer to a question of E.A. Michael is given: A convex $G_\delta$-subset $Y$ of a Hilbert space is constructed together with a l.s.c. map $Y\to Y$ having closed convex values and no continuous selection.
Classification : 54C65
Keywords: l.s.c. map; selection; space of probability measures 
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Filippov, Vladimir V. On a question of E.A. Michael. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 735-737. http://geodesic.mathdoc.fr/item/CMUC_2004__45_4_a12/