Pointed Gromov-Hausdorff Topological Stability for non-compact metric spaces

2022/04/13 by Luis Eduardo Osorio Acevedo, Acevedo, Luis Eduardo Osorio, Henry Mauricio Sánchez Sanabria +1
Mathematics · Medicine · #37B99 #51F99 #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #Neurogenetic and Muscular Disorders Research

paper · pdf · doi:10.48550/arxiv.2204.06649

openalex publication_date 2022/04/13 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28

Abstract

We combine the pointed Gromov-Hausdorff metric [Ron10] with the locally C⁰ distance to obtain the pointed C⁰-Gromov-Hausdorff distance between maps of possibly different non-compact pointed metric spaces. The latter is then combined with Walters's locally topological stability [LNY18] and GH-stability from [AMR17] to obtain the notion of topologically GH-stable pointed homeomorphism. We give one example to show the difference between the distance when take different base point in a pointed metric space.

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