Quantum, classical and intermediate II: the vanishing vector space structure

We propose an approach where physical entities are described by the set of their states, and the set of their relevant 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 ε-example. This leads us to a model for a continuous evolution from the linear closure in vector space to the standard topological closure.