Geodesic
$\Sigma$-products and selections of set-valued mappings
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 203-207

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Every lower semi-continuous closed-and-convex valued mapping $\Phi : X\rightarrow 2^{Y}$, where $X$ is a $\Sigma$-product of metrizable spaces and $Y$ is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.
Classification : 54B10, 54C60, 54C65, 54D15
Keywords: set-valued mapping; l.s.c. mapping; $\Sigma$-product; selection 
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Shishkov, Ivailo. $\Sigma$-products and selections of set-valued mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 203-207. http://geodesic.mathdoc.fr/item/CMUC_2001__42_1_a15/