Igor Arrieta

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20242026

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math.GN2026

The lattice of smooth sublocales as a Bruns-Lakser completion

Igor Arrieta, Anna Laura Suarez

We characterise the frame morphisms $f : L \to M$ that lift to frame maps $f : S_{b} (L) \to S_{b} (M)$ , where $S_{b} (L)$ is the collection of joins of comp…

math.GN2025

Joins of closed sublocales are not always a coframe

Igor Arrieta

Given a locale $L$ , the collection $S_{c} (L)$ of joins of closed sublocales forms a frame--somewhat unexpectedly, as it is naturally embedded in the coframe of all sublocale…

math.GN2024

The DeMorganization of a locale

Igor Arrieta

In 2009, Caramello proved that each topos has a largest dense subtopos whose internal logic satisfies De Morgan law (also known as the law of the weak excluded middle). This findin…

math.GN2023

Localic separation and the duality between closedness and fittedness

Igor Arrieta

There are a number of localic separation axioms which are roughly analogous to the $T_{1}$ -axiom from classical topology. For instance, besides the well-known subfitness and fitness,…