正交模格的内禀拓扑
An Intrisic Topology for Orthomodular Lattices
摘要：
给出了正交模格上拓扑的一般定义方法。我们表明，在希尔伯特格的情况下，这种拓扑结构是等价的，诱导相应的希尔伯特空间的度量。此外，我们表明，在布尔代数的情况下，得到的拓扑是离散的。因此，我们的结构提供了一个通用的工具，研究正交模格，也是一种方法来区分经典和量子逻辑。
英文摘要：
We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.
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