New York Journal of Mathematics
Volume 26 (2020), 1064-1092


Carmelo Antonio Finocchiaro and Dario Spirito

Suprema in spectral spaces and the constructible closure

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Published: September 18, 2020.
Keywords: Spectral spaces; constructible topology; specialization order; overrings; semistar operations.
Subject: 13F05, 13G05, 13C99, 54F05.

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 examine 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.


The authors would like to express their sincere gratitude to the referee, whose remarkable suggestions helped to significantly improve the paper.

Author information

Carmelo Antonio Finocchiaro:
Dipartimento di Matematica e Informatica
Universitá degli Studi di Catania
Viale Andrea Doria 6 - 95125, Catania


Dario Spirito:
Dipartimento di Matematica e Fisica
Universitá degli Studi Roma Tre
Largo San Leonardo Murialdo 1, 00146, Roma;
Current address: Dipartimento di Matematica "Tullio Levi-Civita"
Universitá di Padova
Via Trieste, 63, 35121, Padova