Whitney’s extension problem in o-minimal structures

• Matthias Aschenbrenner ^[1] ; Athipat Thamrongthanyalak ^[2]
  1. [1] University of California Los Angeles

     University of California Los Angeles

     Estados Unidos

     
  2. [2] Chulalongkorn University

     Chulalongkorn University

     Tailandia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 4, 2019, págs. 1027-1052
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In 1934, H. Whitney asked how one can determine whether a real-valued function on a closed subset of Rn is the restriction of a Cm-function on Rn. A complete answer to this question was found much later by C. Fefferman in the early 2000s. Here, we work in an o-minimal expansion of a real closed field and solve the C1-case of Whitney's extension problem in this context. Our main tool is a definable version of Michael's selection theorem, and we include other another application of this theorem, to solving linear equations in the ring of definable continuous functions.