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A geometric proof of the definability of Hausdorff limits. (English) Zbl 1059.03031
Summary: 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 explicitly describes the family of all Hausdorff limits in terms of the original family.

MSC:
03C64 Model theory of ordered structures; o-minimality
14P15 Real-analytic and semi-analytic sets
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