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Peer reviewed
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Acevedo, Luis Eduardo Osorio; Sánchez, Henry Mauricio
Qualitative theory of dynamical systems, 12/2023, Volume: 22, Issue: 4Journal Article
We combine the pointed Gromov-Hausdorff metric with the locally C 0 -distance to obtain the pointed C 0 -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 GH -stability from Arbieto-Morales to obtain the notion of topologically GH -stable pointed homeomorphism. We give one example to show the difference between the distance when taking different base points in a pointed metric space.
