2022/08/22 by Nicolò Zava, Zava, Nicolò
Computer Science · Mathematics · #51F30 #53C23 #54D35 #54E35 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Metric Geometry (math.MG) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2208.10619
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the stability of the q-hyperconvex hull of a quasi-metric space, adapting known results for the hyperconvex hull of a metric space. To pursue this goal, we extend well-known metric notions, such as Gromov-Hausdorff distance and rough isometries, to the realm of quasi-metric spaces. In particular, we prove that two q-hyperconvex hulls are close with respect to the Gromov-Hausdorff distance if so are the original spaces. Moreover, we provide an intrinsic characterisation of those spaces that are Sym-large in their q-hyperconvex hulls.