  Aim of this paper is to develop a new technique, based on the Baire category
theorem, in order to establish the closure of reachable sets and the existence
of optimal trajectories for control systems, without the usual convexity
assumptions. The bang-bang property is proved for a new class of ``concave"
multifunctions, characterized by the existence of suitable linear selections.
The proofs rely on Lyapunov's theorem in connection with a Baire category
argument.
