A construction analogous to that of Godefroy-Kalton for metric spaces allows one to embed isometrically, in a canonical way, every quasi-metric space (X, d) in an asymmetric normed space F-a (X, d) (its quasi-metric free ...

In this note we combine the dyadic families introduced by M. Christ in (Colloq. Math. 60/61(2):601-628, 1990) and the discrete partitions introduced by J.M. Wu in (Proc. Am. Math. Soc. 126(5):1453-1459, 1998) to get ...

What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T0 or T1, but not T2 (i.e. not Hausdorff)? This question has been addressed by Selivanov in ...

In this chapter we give an equivalent point of view for quasi-metricstructures on a set X in terms of families of neighborhoods of the diagonal in X×X.We use this approach and the iterative process introduced by R. Macías ...

Caracterizamos, em termos de equações diferenciais, as métricas = , conformes à métrica pseudo-Euclidiana , que são quasi-Einstein. Para um campo de vetores (não-Killing) especial, o sistema de e4quações reduz-se a uma ...

Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under ...

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a ...

We introduce and study the Lipschitz injective hull of Lipschitz operator ideals defined between metric spaces. We show some properties and apply the results to the ideal of Lipschitz p-nuclear operators, obtaining the ...