A Theory of Finite Closure Spaces Based on Implications
A Theory of Finite Closure Spaces Based on Implications
复制标题
基于蕴涵的有限闭空间理论
DOI：
10.1006/aima.1994.1069
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发表时间：
1994
影响因子：
1.7
通讯作者：
M. Wild
中科院分区：
文献类型：
--
作者：
M. Wild
摘要尽管拓扑和矩形理论所熟悉的许多概念对于任意封闭空间来说是有意义的，但我们声称“含义基础”是最值得研究的。它们应用于关系数据基础理论和正式概念分析。在组合和代数中的进一步应用是可预见的。主要定理描述了任何有限闭合空间的最小值，最佳，含义的基础的结构。它具有针对特定闭合空间的强大推动性，例如，具有封闭组的几何，模块化，分别较低的分布晶格。
Abstract Although many notions familiar from topology and matroid theory make sense for arbitrary closure spaces, we claim that "implicational bases" are most worthwhile studying. They are applied in the theory of relational data bases and in formal concept analysis. Further applications in combinatorics and algebra are foreseeable. The main theorem describes the structure of minimum, respectively optimal, implicational bases of any finite closure space. It has strong corollaries for specific closure spaces, e.g., having a geometric, respectively modular, respectively lower distributive, lattice of closed sets.