  We show that the natural mathematical structure to describe a physical entity
by means of its states and its properties within the Geneva-Brussels approach
is that of a state property system. We prove that the category of state
property systems (and morphisms), SP, is equivalent to the category of closure
spaces (and continuous maps), Cls. We show the equivalence of the 'state
determination axiom' for state property systems with the 'T0 separation axiom'
for closure spaces. We also prove that the category SP0 of state determined
state property systems is equivalent to the category L0 of based complete
lattices. In this sense the equivalence of SP and Cls generalizes the
equivalence of Cls0 and L0, proven in Erne 1984.
