状态属性系统与闭包空间：范畴等价的研究
State property systems and closure spaces: a study of categorical equivalence
摘要：
我们表明，自然的数学结构来描述一个物理实体，通过其状态和属性在日内瓦-布鲁塞尔的方法是一个国家的财产制度。我们证明了范畴的状态属性系统（和态射），SP，是等价于范畴的闭包空间（和连续映射），Cls。我们证明了状态属性系统的“状态决定公理”与闭包空间的“T0分离公理”的等价性。我们还证明了状态决定的状态属性系统的范畴SP 0等价于基完备格的范畴L 0。在这个意义上，SP和Cls的等价性推广了Cls 0和L0的等价性，这在Erne 1984中得到了证明。
英文摘要：
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.
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