Geodesic
Connectedness of the solution sets of inclusions
Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 836-861
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A research scheme for investigating the connectedness of the set of solutions of an inclusion in a topological space is proposed. It is applied to analyze the fixed-point set of a Volterra set-valued map in the space of continuous functions $C$; conditions for it to be connected in the norm and weak topology of $C$ are obtained. On this basis conditions are found which ensure that the solution set of Hammerstein's delay integral inclusion is connected. Bibliography: 14 titles.
Keywords: connectedness, topological space, Volterra set-valued map, fixed point. 
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E. S. Zhukovskiy. Connectedness of the solution sets of inclusions. Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 836-861. http://geodesic.mathdoc.fr/item/SM_2019_210_6_a3/

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