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On the topological regularity of the solution set of differential inclusions with constraints. (English) Zbl 0796.34017
This paper deals with the topological regularity of the solution set of differential inclusions. In particular, it is proved that the solution set of differential inclusions with constraints is an $$R\delta$$ set in the case of the space $$\mathbb{R}^ n$$, and nonempty compact and connected set in the case of a Banach space. The main tool of the proof is an approximation result by Lipschitz functions the Carathéodory functions, also given in this paper.

##### MSC:
 34A60 Ordinary differential inclusions
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