A Dual Characterization of Subdirectly Irreducible BAOs
A Dual Characterization of Subdirectly Irreducible BAOs
复制标题
次不可约 BAO 的双重表征
DOI：
10.1023/b:stud.0000034188.80692.46
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发表时间：
2004
期刊：
影响因子：
0.7
通讯作者：
Y. Venema
中科院分区：
文献类型：
--
作者：
Y. Venema
我们用对偶描述框架或拓扑关系结构给出了简单布尔代数和带算子的子直接不可约布尔代数（包括模态代数）的刻画。这些表征涉及到对偶结构上的一种特殊的二元拓扑可达关系；如果每个超滤波器都从u拓扑可达，我们称点u为对偶结构的拓扑根。我们证明了带算子的布尔代数是简单的，如果对偶结构中的每个点都是拓扑根；如果拓扑根集合在对偶结构的Stone拓扑中是开放且非空的，则该拓扑根集合在该拓扑中具有非空的内部，则该拓扑根集合是子直接不可约的。
We give a characterization of the simple, and of the subdirectly irreducible boolean algebras with operators (including modal algebras), in terms of the dual descriptive frame, or, topological relational structure. These characterizations involve a special binary topo-reachability relation on the dual structure; we call a point u a topo-root of the dual structure if every ultrafilter is topo-reachable from u. We prove that a boolean algebra with operators is simple iff every point in the dual structure is a topo-root; and that it is subdirectly irreducible iff the collection of topo-roots is open and non-empty in the Stone topology on the dual structure iff this collection has non-empty interior in that topology.