Аннотация:Hybrid systems are interacting networks of real time digital programs, implemented as finite automata, and continuous physical systems, usually referred to as plants. The purpose of the real time digital programs is to control the behavior of the plants. Our purpose is to introduce a topological semantics for hybrid systems so that proofs of digital program correctness imply that behavior is correct in the presence of fluctuations in critical parameters such as observation of plant state. This is not provided by existing languages for non-linear plants.