Quantum axiomatics: Topological properties and classical properties of state property systems

The definition of 'classical state' to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property lattice of a physical system. In this paper we argue on the basis of the epsilon-model on the Bloch-sphere that a notion of 'topologicity' for states can be seen as an alternative 'operationally foundable' classicality notion in the absence of an orthocomplementation, and compare it to the known and operationally founded concept of classicality.