Abstract
A small topic in the abstract theory of system modelling is investigated in this paper. As understood here, a system is a map F from an input space U to an output space Y. The systems with which we are concerned are causal dynamical systems for which inputs and outputs are functions of time. The topic under consideration is the choice and topologization of input and output spaces and their relation to system behavior. The concepts described below, which underlie the work in [1] and [2], provide intuitive background for the development here. Let y = F(u) be the input-output map of a causal (in general of a nonlinear, time-varying) system, where u and y are functions of time belonging to suitable function spaces U and Y, respectively, and F is causal, continuous and bounded. Let Pt, t ~ R , denote projection on the past; i.e. for any function of time z, (Ptz)(s) = z(s) or 0 according as s t. Fix T > 0 and define fit for all t ~ R by
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