8 citations · 24 across the 18 of their papers we have counts for
19 papers
Polynomials over idempotent semifields
Paul Poncet
We study univariate polynomials with coefficients in an idempotent semifield and their factorization. We do not assume the idempotent semifield under consideration to be totally or…
Order-generation in posets and convolution of closure operators
Paul Poncet
Motivated by the Hofmann--Lawson theorem, which states that every continuous lattice is inf-generated by its irreducible elements, we explore how to represent posets by extreme poi…
Partial metrics and normed inverse semigroups
Paul Poncet
Relying on the notions of submodular function and partial metric, we introduce normed inverse semigroups as a generalization of normed groups and sup-semilattices equipped with an…
A memo on bornologies and size functions
Paul Poncet
We recall the notion of abstract bornology, and connect it with topological spaces and size functions. As a generalization of measures of non-compactness, we show how every size fu…
Galois connections between closure spaces
Paul Poncet
Galois connections were introduced by Ore and have proved useful in a wide variety of mathematical areas. While Galois connections play on the ground of posets (or more generally o…
Enriched closure spaces as a novel framework for domain theory
Paul Poncet
We propose a generalization of continuous lattices and domains through the concept of enriched closure space, defined as a closure space equipped with a preclosure operator satisfy…