谱空间中的上实与可构造闭包
Suprema in spectral spaces and the constructible closure
摘要：
给定一个谱空间$X$，赋予它特殊化序$\leq$，研究了$(X,\leq)$的子集上确界与可构造拓扑之间的相互作用.更准确地说，我们调查的上确界时，一个集$Y\subseteq X$存在，并属于$Y$的可构造闭包。我们将这些结果应用到代数格的集合和闭包运算，证明了一些著名的空间的环和理想的密度性质。此外，我们还利用理想的拓扑性质给出了某些整环的拓扑刻画。
英文摘要：
Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the supremum of a set $Y\subseteq X$ exists and belongs to the constructible closure of $Y$. We apply such results to algebraic lattices of sets and to closure operations on them, proving density properties of some distinguished spaces of rings and ideals. Furthermore, we provide topological characterizations of some class of domains in terms of topological properties of their ideals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
