Topological Spaces in the Systems Theory

The continuity is a common concept, often used by people. It is not the case of topology, although behind the phenomenon of continuity always a topology must be understood. In a continuous process, if two possible causes remain close, that is in a certain neighborhood, they will produce close effects. The set of possible causes which lead to a studied effect is organized as a topological space. Researchers can deal with metric spaces, with norms or semi-norms, but it is important to establish the notion of neighborhood, or to define a system of open sets. In the study of dynamic systems with infinite memory a locally convex topology was introduced. The present paper reviewed results obtained when the inputs were continuous and indefinite derivable functions from minus infinite to the present moment, then it pass to the case when the inputs are known only as rows of values. In the last part the informational topology is exposed.