5 citations · 8 across the 5 of their papers we have counts for
6 papers
Overlap Algebras: a Constructive Look at Complete Boolean Algebras
Francesco Ciraulo, Michele Contente
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a g…
-locales in Formal Topology
Francesco Ciraulo
A -frame is a poset with countable joins and finite meets in which binary meets distribute over countable joins. The aim of this paper is to show that -frames, actually -l…
Overlap Algebras as Almost Discrete Locales
Francesco Ciraulo
Boolean locales are "almost discrete", in the sense that a spatial Boolean locale is just a discrete locale (that is, it corresponds to the frame of open subsets of a discrete spac…
Convergence in Formal Topology: a unifying notion
Francesco Ciraulo, Maria Emilia Maietti, Giovanni Sambin
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that o…
Constructive version of Boolean algebra
Francesco Ciraulo, Maria Emilia Maietti, Paola Toto
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: w…
A constructive Galois connection between closure and interior
Francesco Ciraulo, Giovanni Sambin
We construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of…