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

Luis Eduardo Osorio Acevedo, Henry Mauricio Sánchez

• 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.