Bitopological duality for distributive lattices and Heyting algebras
Bitopological duality for distributive lattices and Heyting algebras
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DOI：
10.1017/s0960129509990302
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发表时间：
2010-01
影响因子：
0.5
通讯作者：
G. Bezhanishvili;N. Bezhanishvili;D. Gabelaia;A. Kurz
中科院分区：
文献类型：
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作者：
G. Bezhanishvili;N. Bezhanishvili;D. Gabelaia;A. Kurz
我们引入成对Stone空间作为Stone空间（布尔代数的对偶）的双拓扑推广，并证明它们正是有界分配格的双拓扑对偶。成对Stone空间的范畴PStone同构于谱空间的范畴Spec和Priestley空间的范畴Pries。事实上，同构的规范和普利斯是最自然地看到通过PStone首先建立普利斯是同构的PStone，然后显示PStone是同构的规范。我们提供了双拓扑和频谱描述的许多代数概念的重要研究分配格。我们还给出了新的双拓扑和谱对偶的Heyting代数，从而提供了两个新的替代Esakia的对偶。
We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces – the duals of Boolean algebras – and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important in the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, thereby providing two new alternatives to Esakia's duality.