Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2004, October 12.

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-Haudorff limit is taken with respect to the geodesic metric and the word {\it definable} means {\it definable in some o-minimal structure over $\R$.

Mathematics Subject Classification (2000): 14P10, 53C23.

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