Une procédure de complétion transfinie pour les espaces métriques
Year: 2026
Type: conference-abstract
Abstract: This poster studies a notion arising from the theory of interpolation spaces extended to metric spaces. To compensate for the lack of algebraic structure in this setting, the constructions introduced in [1, 3] share a common underlying principle, leading to a natural way of extending a metric space A within a metric space B. This extension procedure has never been investigated in a systematic framework. As a consequence, some fundamental questions remain unanswered. In particular, it is referred to as a “completion”, although it can yield a non-complete space. Therefore, existing approaches provide only a partial understanding of the construction. In this work, we develop a general theory of this procedure which we call the Cauchy extension. In particular, we will present an example of a metric space with a non-complete Cauchy extension. Furthermore, in analogy with the Cantor-Bendixson theorem [2], we will provide a genuine completion procedure by showing that iterating the Cauchy extension along ordinals always stabilizes at a complete metric space.
Source: ORBi (University of Liège)
Author: Bertrand, Hugo
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163722236