Summary: We propose an approach where physical entities are described by the set of their states, and the set of their relevalent experiments. In this framework we will study a general entity that is neither quantum nor classical. We show that the collection of eigenstate sets forms a closure structure on the set of states. We also illustrate this framework on a concrete physical example, the \(\varepsilon \)-example. This leads us to a model for a continuous evolution from the linear closure in a vector space to the standard topological closure.
For Part I see the review above.