论文标题
通过某些禁止配置来表征可元的esakia空间
Characterization of metrizable Esakia spaces via some forbidden configurations
论文作者
论文摘要
通过Priestley二元性，每个有界的分布晶格被表示为Priestley空间的clopen Upset的晶格，而Esakia Duality则表示，每个Heyting代数都被表示为Esakia空间的Clopen Upsets的晶格。爱esakia的空间是那些满足每个clopen降低的额外条件的普里斯特利空间。我们表明，在可计算的情况下，可以通过禁止三种简单配置来挑选Esakia空间。由于衡量性产生的clopen Upset的相应晶格是可计数的，因此这提供了可数的Heyting代数的表征。我们表明，这种特征在不可数的情况下不再存在。我们的结果具有用于共同呼吸代数和双向代数的类似物，并且它们很容易推广到p-Elgebras的设置。
By Priestley duality, each bounded distributive lattice is represented as the lattice of clopen upsets of a Priestley space, and by Esakia duality, each Heyting algebra is represented as the lattice of clopen upsets of an Esakia space. Esakia spaces are those Priestley spaces that satisfy the additional condition that the downset of each clopen is clopen. We show that in the metrizable case Esakia spaces can be singled out by forbidding three simple configurations. Since metrizability yields that the corresponding lattice of clopen upsets is countable, this provides a characterization of countable Heyting algebras. We show that this characterization no longer holds in the uncountable case. Our results have analogues for co-Heyting algebras and bi-Heyting algebras, and they easily generalize to the setting of p-algebras.
