Assouad's theorem with dimension independent of the snowflaking

Details Assouad's theorem with dimension independent of the snowflaking Assouad's theorem with dimension independent of the snowflaking

2010-12-10

arxiv.org/abs/1012.2307v1

Mathematics

Metric Geometry

Scientific paper

It is shown that for every $K>0$ and $\e\in (0,1/2)$ there exist $N=N(K)\in \N$ and $D=D(K,\e)\in (1,\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\e})$ admits a bi-Lipschitz embedding into $\R^N$ with distortion at most $D$. The classical Assouad embedding theorem makes the same assertion, but with $N\to \infty$ as $\e\to 0$.

Affiliated with

Also associated with

No associations

Rating

Assouad's theorem with dimension independent of the snowflaking does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Assouad's theorem with dimension independent of the snowflaking, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Assouad's theorem with dimension independent of the snowflaking will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108112