State Property Systems and Closure Spaces: A Study of Categorical Equivalence
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We show that the natural mathematical structureto describe a physical entity by means of its states andits properties within the Geneva–Brussels approachis that of a state property system. We prove that the category of state property systems (andmorphisms) SP is equivalent to the category ofclosure spaces (and continuous maps) Cls. We showthe equivalence of the ‘state determinationaxiom’ for state property systems with the ‘T0separation axiom’ for closure spaces. We alsoprove that the category SP0 ofstate-determined state property systems is equivalent tothe category L0 of based completelattices. In this sense the equivalence of SP andCls generalizes the equivalence ofCls0 (T0 closure spaces)and L0 proven by Erne(1984).
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