拓扑正交代数
Topological Orthoalgebras
摘要：
定义了拓扑正交代数并研究了它们的性质。虽然每个拓扑正交模格都是TOA，但希尔伯特空间的投影格是格序TOA的一个例子，它不是拓扑格。另一方面，我们证明了每个紧布尔TOA是一个拓扑布尔代数。我们还表明，一个紧凑的TOA，其中0是一个孤立的点是原子和有限的高度。我们确定和研究一类特别容易处理的TOA，我们称之为{ \em稳定有序}：那些在其中由开集生成的上集是开放的。这包括所有拓扑OML，也包括希尔伯特空间的投影格。最后，我们得到了稳定有序TOA的Foulis-Randall表示论的拓扑形式
英文摘要：
We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show that a compact TOA in which 0 is an isolated point is atomic and of finite height. We identify and study a particularly tractable class of TOAs, which we call {\em stably ordered}: those in which the upper-set generated by an open set is open. This includes all topological OMLs, and also the projection lattices of Hilbert spaces. Finally, we obtain a topological version of the Foulis-Randall representation theory for stably ordered TOAs
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