Geodesic
Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 533-538

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Every l.s.c\. mapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) $G_\delta $-subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.
Classification : 46B20, 46N10, 54C60, 54C65, 54F45
Keywords: set-valued mapping; lower semi-continuous; upper semi-continuous; selection; countable-dimensional space 
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Gutev, Valentin G. Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 533-538. http://geodesic.mathdoc.fr/item/CMUC_1994__35_3_a10/