Suprema in spectral spaces and the constructible closure

2019/06/17 by Carmelo Antonio Finocchiaro, Finocchiaro, Carmelo Antonio, Dario Spirito +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1906.07053

openalex publication_date 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an arbitrary spectral space X, we endow it with its specialization order ≤ and we study the interplay between suprema of subsets of (X,≤) and the constructible topology. More precisely, we investigate about when the supremum of a set Y⊆ 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.

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• Closure operators on semilattice-ordered semigroups and spectrality of induced operations

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