On the continuity property of balls and an application

Abstract: In this paper continuity properties of the set-valued map , , are considered where is the closed ball of the space centered at the origin with radius . It is proved that the set-valued map , , is continuous. Applying obtained results, the attainable set of the nonlinear control system with integral constraint on the control is studied. The admissible control functions are chosen from . It is shown that the attainable set of the system is continuous with respect to p. [Copyright &y& Elsevier]