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arXiv · 2204.06649

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

Luis Eduardo Osorio Acevedo·Henry Mauricio Sánchez Sanabria
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Abstract

We combine the pointed Gromov-Hausdorff metric [Ron10] 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 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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Luis Eduardo Osorio Acevedo, Henry Mauricio Sánchez Sanabria. 2022-04-13. Pointed Gromov-Hausdorff Topological Stability for non-compact metric spaces. https://arxiv.org/abs/2204.06649

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