16 citations · 35 across the 24 of their papers we have counts for
6 papers · 1 filter
The Golomb space is topologically rigid
Taras Banakh, Dario Spirito, Sławomir Turek
The is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions $\{a+bn:n\g…
The Golomb topology of polynomial rings
Dario Spirito
We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show t…
Multiplicative closure operations on ring extensions
Dario Spirito
Let be a ring extension and be a set of -submodules of . We introduce a class of closure operations on (which we call \emph{multipl…
The Golomb topology on a Dedekind domain and the group of units of its quotients
Dario Spirito
We study the Golomb spaces of Dedekind domains with torsion class group. In particular, we show that a homeomorphism between two such spaces sends prime ideals into prime ideals an…
Suprema in spectral spaces and the constructible closure
Carmelo Antonio Finocchiaro, Dario Spirito
Given an arbitrary spectral space , we endow it with its specialization order and we study the interplay between suprema of subsets of and the constructible to…
Extending valuations to the field of rational functions using pseudo-monotone sequences
Giulio Peruginelli, Dario Spirito
Let be a valuation domain with quotient field . We show how to describe all extensions of to when the -adic completion is algebraically closed, g…