Abstract
The notion of piecewise definable metric space is introduced. It is shown that the set of all Gromov-Hausdorff limits of piecewise definable spaces belonging to a fixed bounded definable family is again a definable family. The Gromov-Hausdorff limit is taken with respect to the geodesic metric and the word definable means definable in some o-minimal structure over $\mathbb{R}$.
Citation
Andreas Bernig. "Gromov-Hausdorff limits in definable families." Illinois J. Math. 49 (2) 475 - 485, Summer 2005. https://doi.org/10.1215/ijm/1258138029
Information