原子格效应代数的几乎正交性和Hausdorff区间拓扑
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
摘要：
证明了当$E$的所有原子的集合几乎正交时，阿基米德原子格效应代数$E$的区间拓扑是Hausdorff的.在这种情况下，$E$是阶连续的。此外，如果$E$是完整的，那么$E$的元素网的顺序收敛是拓扑的，因此它与顺序拓扑中的收敛一致，并且这个拓扑是紧的Hausdorff相容的，与$E$上对应于紧和余紧元素的分离函数族引起的一致性相容。对于块有限阿基米德原子格效应代数，证明了几乎正交性与s-紧生成的等价性。作为主要应用，我们得到了这些效应代数的状态涂抹定理，以及$\oplus$ -运算在序拓扑和区间拓扑上的连续性。
英文摘要：
We prove that the interval topology of an Archimedean atomic lattice effect algebra $E$ is Hausdorff whenever the set of all atoms of $E$ is almost orthogonal. In such a case $E$ is order continuous. If moreover $E$ is complete then order convergence of nets of elements of $E$ is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on $E$ corresponding to compact and cocompact elements. For block-finite Archimedean atomic lattice effect algebras the equivalence of almost orthogonality and s-compact generation is shown. As the main application we obtain the state smearing theorem for these effect algebras, as well as the continuity of $\oplus$-operation in the order and interval topologies on them.
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