Pointed Gromov-Hausdorff Topological Stability for Non-compact Metric Spaces

• Luis Eduardo Osorio Acevedo ^[1] ; Henry Mauricio Sánchez ^[2]
  1. [1] Universidad Tecnológica de Pereira

     Universidad Tecnológica de Pereira

     Colombia

     
  2. [2] Universidad Central, Bogotá
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
• Idioma: inglés
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• Resumen

  • We combine the pointed Gromov-Hausdorff metric 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 combined with Walters’s locally topological stability proposed by Lee–Nguyen–Yang, and G H-stability from ArbietoMorales to obtain the notion of topologically G H-stable pointed homeomorphism. We give one example to show the difference between the distance when taking different base points in a pointed metric space.