arXiv subjects

Jesús Rodríguez-López

Publications and source records attributed to Jesús Rodríguez-López.

5 recordsLinked to original sources

arXiv2026

Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories

We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also show that, by means of this isomorphism, the topology associated with a quasi-pseudometric modular coincides with that generated by its corresponding quantale enriched category. Furthermore, we demonstrate that the class of quasi-pseudometrizable topological spaces coincides with the topological spaces whose topology is induced by a quasi-pseudometric modular.

math.CT↗

arXiv2026

Aggregation functions as lax morphisms of quantales

We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the study of aggregation functions. As a consequence of our theory, we are able to deduce several known results about the aggregation of metrics and fuzzy metrics.

math.CT↗

arXiv2026

A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps

In the paper [E. Jiménez-Fernández, J. Rodr\'ıguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space $(\mathbb{R},M_{ϕ,g},\ast).$ However, while the function $ϕ$ is only required to be increasing, some results of the paper implicitly assume that $ϕ$ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires $ϕ$ to be also left-continuous.

math.GM↗

arXiv2026

Strongly quasi-pseudometric aggregation functions

Metric-preserving functions (here, metric aggregation functions) offer a natural method for constructing metrics on Cartesian products of metric spaces or for aggregating multiple metrics defined on a common set. Strongly metric-preserving functions represent a more specialized subset of these functions, ensuring that the new metric aligns with the product topology, in the Cartesian product case. However, these strong functions have not been previously explored for quasi-pseudometrics. Furthermore, in the case where all metrics are defined on the same set, the problem has not been addressed previously. In this paper, we investigate the class of strongly (quasi-)(pseudo)metric aggregation functions, extending the classical concept. We begin by examining the case where the aggregation function produces (quasi-)(pseudo)metrics on Cartesian products, characterizing these functions through continuity at zero and a minimal zero preimage condition. In addition, we will examine the scenario where the aggregation function produces a (quasi-)(pseudo)metric defined on a fixed set. Within this context, we will demonstrate that the appropriate topology to consider is the supremum topology. We will also provide both necessary and sufficient conditions for an (quasi-)(pseudo)metric aggregation function on sets to qualify as a strongly one, thereby addressing a gap in the existing literature.

math.GN↗

arXiv2025

New results about aggregation functions of quasi-pseudometric modulars

In recent studies, Bibiloni-Femenias, Miñana and Valero characterized the functions that aggregate a family of (quasi-)(pseudo)metric modulars defined over a fixed set $X$ into a single one. In this paper, we adopt a related but different approach to examine those functions that allow us to define a (quasi-)(pseudo)metric modular in the Cartesian product of (quasi-)(pseudo)metric modular spaces. We base our research on the recent development of a general theory of aggregation functions between quantales. This enables to shed light between the two different ways of aggregation (quasi-)(pseudo)metric modulars.

math.GN↗