Geodesic
Continuous selection theorems
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 25 (2005) no. 1, pp. 159-163

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Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
Keywords: set-valued mappings, continuous selection, Fillipov's selection theorem, 
Kisielewicz, Michał. Continuous selection theorems. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 25 (2005) no. 1, pp. 159-163. http://geodesic.mathdoc.fr/item/DMDICO_2005_25_1_a7/
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[1] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ., New York 1991.

[2] E. Michael, Continuous selections, Annales Math. 63 (1956), 361-382.

[3] L. Rybiński, On Carathéodory type selections, Fund. Math. 125 (1985), 187-193.