  We introduce classical properties using the concept of super selection rule,
i.e. two properties are separated by a superselection rule iff there do not
exist 'superposition states' related to these two properties. Then we show that
the classical properties of a state property system correspond exactly to the
clopen subsets of the corresponding closure space. Thus connected closure
spaces correspond precisely to state property systems for which the elements 0
and I are the only classical properties, the so called pure nonclassical state
property systems. The main result is a decomposition theorem, which allows us
to split a state property system into a number of 'pure nonclassical state
property systems' and a 'totally classical state property system'. This
decomposition theorem for a state property system is the translation of a
decomposition theorem for the corresponding closure space into its connected
components.
