A geometric proof of the definability of Hausdorff limits

• J.M. Lion ^[2] ; P. Speissegger ^[1]
  1. [1] McMaster University

     McMaster University

     Canadá

     
  2. [2] UFR Mathématiques, Université de Rennes 1, Francia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 3, 2004, págs. 377-390
• Idioma: inglés
• DOI: 10.1007/s00029-004-0360-z
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• Resumen

  • 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.