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Whitney's Example by Way of Assouad's Embedding
Proceedings of the American Mathematical Society
Vol. 131, No. 11 (Nov., 2003), pp. 3463-3467
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1194654
Page Count: 5
You can always find the topics here!Topics: Mathematical functions, Mathematical theorems, Mathematical constants, Cubes, Partial derivatives, Embeddings, Euclidean space, Topological theorems, Continuous functions
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In this note we show how to use the Assouad embedding theorem (about almost bi-Lipschitz embeddings) to construct examples of Cm 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.
Proceedings of the American Mathematical Society © 2003 American Mathematical Society