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

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. [ABSTRACT FROM AUTHOR]