To each discrete dynamical system (X; f), we may as- sociate, in a natural way, a "functional" discrete dynamical system (C(X;X); f) whose phase space C(X;X) is the set of all continuous self-maps on X endowed with a suitable topology. In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of 'light chaos' is the most significant. Several examples, which clarify the relationships between this kind of chaos and some classical notions, are given. Particular attention is also devoted to the connections between the dynamical properties of a system and the dynamical properties of the associated functional envelope. We show, among other things, that a continuous self-map on a metric space X is chaotic (in the sense of Devaney) if and only if the associated functional envelope is lightly chaotic.