关联结构与Stone-Priestley对偶
Incidence structures and Stone-Priestley duality
摘要：
我们观察到，如果$R:=(I,ρ, J)$是一个关联我们观察到，如果$R:=(I,ρ, J)$是一个关联结构，视为一个矩阵，那么列集的拓扑闭包是由行生成的布尔代数的斯通空间。由此得到偏序集$P$的主初始段集的拓扑闭包是由$P$的主终段集生成的布尔代数$Tailalg (P)$的Stone空间，即所谓的{$P$的\it尾代数}.对Priestley空间和分配格也给出了类似的结果。抽象代数值的关联结构被认为是一个推广。
英文摘要：
We observe that if $R:=(I,ρ, J)$ is an incidence We observe that if $R:=(I,ρ, J)$ is an incidence structure, viewed as a matrix, then the topological closure of the set of columns is the Stone space of the Boolean algebra generated by the rows. As a consequence, we obtain that the topological closure of the collection of principal initial segments of a poset $P$ is the Stone space of the Boolean algebra $Tailalg (P)$ generated by the collection of principal final segments of $P$, the so-called {\it tail-algebra of $P$}. Similar results concerning Priestley spaces and distributive lattices are given. A generalization to incidence structures valued by abstract algebras is considered.
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