Real Algebraic and Analytic Geometry

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31. Jean-Marie Lion, Patrick Speissegger:
A geometric proof of the definability of Hausdorff limits.

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Submission: 2003, February 6.

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.: dvi 73k, ps.gz 71k, pdf 228k.

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