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We give a denotational framework for composing interactive components into closed or open systems and show how to adapt classical domain-theoretic approaches to open systems and to timed systems. For timed systems, instead of the usual metric-space-based approaches, we show that existence and uniqueness of behaviors are ensured by continuity with respect to a simply defined prefix order. Existence and uniqueness of behaviors, however, does not imply that a composition of components yields a useful behavior. The unique behavior could be empty or smaller than expected. We define liveness and show that appropriately defined causality conditions ensure liveness and freedom from Zeno conditions. In our formulation, causality does not require a metric and can embrace a wide variety of models of time.

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