A Note on Hilbert Algebras and Their Related Generalized Esakia Spaces
A Note on Hilbert Algebras and Their Related Generalized Esakia Spaces
复制标题
希尔伯特代数及其相关广义Esakia空间的注记
DOI：
10.1007/s11083-015-9378-4
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发表时间：
2016
期刊：
影响因子：
0.4
通讯作者：
R. Jansana
中科院分区：
文献类型：
--
作者：
S. Celani;R. Jansana
广义Esakia空间是G.Bezhanishvili和R.Jansana研究的对偶中有界关联半格的拓扑对偶。研究了Hilbert代数与其自由蕴涵半格扩张的广义Esakia空间对偶之间的关系。为了建立这种关系，我们引入了一个范畴，它的对象是广义Esakia空间，以及构成广义Esakia空间的Up集的Heyting代数的蕴涵片段的子代数的一族clopup-set。
Generalized Esakia spaces are the topological duals of bounded implicative semilattices in the duality studied by G. Bezhanishvili and R. Jansana. We study the relation between a Hilbert algebra and the generalized Esakia space dual to its free implicative semilattice extension. To establish the relation we introduce a category whose objects are a generalized Esakia space together with a family of clopen up-sets that constitutes a subalgebra of the implication fragment of the Heyting algebra of the up-sets of the generalized Esakia space.