Abstract
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 SP 0 ofstate-determined state property systems is equivalent tothe category L 0 of based completelattices. In this sense the equivalence of SP andCls generalizes the equivalence ofCls 0 (T0 closure spaces)and L 0 proven by Erne(1984).
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Aerts, D., Colebunders, E., Voorde, A.V.D. et al. State Property Systems and Closure Spaces: A Study of Categorical Equivalence. International Journal of Theoretical Physics 38, 359–385 (1999). https://doi.org/10.1023/A:1026657913077
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DOI: https://doi.org/10.1023/A:1026657913077