Whitney’s extension problem in o-minimal structures

  • Matthias Aschenbrenner

    University of California Los Angeles, USA
  • Athipat Thamrongthanyalak

    Chulalongkorn University, Bangkok, Thailand
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Abstract

In 1934, H. Whitney asked how one can determine whether a real-valued function on a closed subset of is the restriction of a -function on . 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 -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.

Cite this article

Matthias Aschenbrenner, Athipat Thamrongthanyalak, Whitney’s extension problem in o-minimal structures. Rev. Mat. Iberoam. 35 (2019), no. 4, pp. 1027–1052

DOI 10.4171/RMI/1077