Gromov-Hausdorff limits in definable families
Bernig, Andreas
Illinois J. Math., Tome 49 (2005) no. 2, p. 475-485 / Harvested from Project Euclid
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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 $\mathbb{R}$.
Publié le : 2005-04-15
Classification:  53C23,  14P10 
@article{1258138029,
     author = {Bernig, Andreas},
     title = {Gromov-Hausdorff limits in definable families},
     journal = {Illinois J. Math.},
     volume = {49},
     number = {2},
     year = {2005},
     pages = { 475-485},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138029}
}

Bernig, Andreas. Gromov-Hausdorff limits in definable families. Illinois J. Math., Tome 49 (2005) no. 2, pp.  475-485. http://gdmltest.u-ga.fr/item/1258138029/