Proceedings of the American Mathematical Society

Author(s): Piotr Hajlasz
Journal: Proc. Amer. Math. Soc. 131 (2003), 3463-3467.
MSC (2000): Primary 26B05; Secondary 26B35, 28A80
Posted: 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

functions which are not constant on a critical set homeomorphic to the

-dimensional cube. This extends the famous example of Whitney. Our examples are shown to be sharp.

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