We introduce a mathematical model of components that can be used for the description of both hardware and software units forming distributed interactive systems. As part of a distributed system a component interacts with its environment by exchanging messages in a time frame. The interaction is performed by accepting input and by producing output messages on named channels. We describe forms of composition and three forms of refinement, namely property refinement, glass box refinement, and interaction refinement. Finally, we prove the compositionality of the mathematical model with respect to the introduced refinement relations.