Real Algebraic and Analytic Geometry |

A geometric proof of the definability of Hausdorff limits.

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Submission: 2003, February 6.

*Abstract:
We give a geometric proof of the following well-established
theorem for o-minimal expansions of the real field: the Hausdorff limits of a
compact, definable family of sets are definable. While previous
proofs of this fact relied on the model-theoretic compactness theorem,
our proof explicitely describes the family of all Hausdorff limits in
terms of the original family.*

Mathematics Subject Classification (2000): 14P15, 03C64.

Keywords and Phrases: o-minimal structures, Hausdorff limits, foliations.

**Full text**, 14p.:
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