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Convergence in formal topology: a unifying notion
We introduce a general notion of convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections in the lattice of opens. Expand
The overlap algebra of regular opens
Abstract Overlap algebras are complete lattices enriched with an extra primitive relation, called “overlap”. The new notion of overlap relation satisfies a set of axioms intended to capture, in aExpand
Finitary formal topologies and Stone's representation theorem
We study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. Expand
Finiteness in a Minimalist Foundation
We analyze the concepts of finite set and finite subset from the perspective of a minimalist foundational theory which is “minimalist” in the sense that it can be seen as the common core of some of the most used foundations. Expand
Constructive version of Boolean algebra
We generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins. Expand
A constructive Galois connection between closure and interior
We construct a Galois connection between closure and interior operators on a given set that is intuitionistically valid. Expand
Eating Pizza to learn fractions
We present "Pizza al Lancio", a serious game to help children understand fractions, in particular equivalent and complementary fractions. Expand
Lindenbaum’s Lemma via Open Induction
With Raoult’s Open Induction in place of Zorn’s Lemma, we do a perhaps more perspicuous proof of Lindenbaum’s Lemma for not necessarily countable languages of first-order predicate logic. WeExpand
Positivity relations on a locale
This paper analyses the notion of a positivity relation of Formal Topology from the point of view of the theory of Locales. Expand
Embedding locales and formal topologies into positive topologies
A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation. Expand