## Whitney’s example by way of Assouad’s embedding

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- by Piotr Hajłasz
- Proc. Amer. Math. Soc.
**131**(2003), 3463-3467 - DOI: https://doi.org/10.1090/S0002-9939-03-06913-2
- Published electronically: February 6, 2003
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## Abstract:

In this note we show how to use the Assouad embedding theorem (about almost bi-Lipschitz embeddings) to construct examples of $C^m$ functions which are not constant on a critical set homeomorphic to the $n$-dimensional cube. This extends the famous example of Whitney. Our examples are shown to be sharp.## References

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## Bibliographic Information

**Piotr Hajłasz**- Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02–097 Warszawa, Poland
- MR Author ID: 332316
- Email: hajlasz@mimuw.edu.pl
- Received by editor(s): October 16, 2001
- Received by editor(s) in revised form: May 29, 2002
- Published electronically: February 6, 2003
- Additional Notes: This work was supported by the KBN grant no. 2 PO3A 028 22.
- Communicated by: Juha M. Heinonen
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 3463-3467 - MSC (2000): Primary 26B05; Secondary 26B35, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-03-06913-2
- MathSciNet review: 1991757