维数与雪花化无关的Assouad定理
Assouad's theorem with dimension independent of the snowflaking
摘要：
证明了对于每个$K>0$和$\e\in (0,1/2)$，都存在具有下列性质的$N=N(K)\in \N$和$D=D(K,\e)\in (1,\infty)$.对于每一个可分度量空间$(X,d)$，其加倍常数至多为$K$，度量空间$(X,d^{1-\e})$允许一个双Lipschitz嵌入到$\R^N$中，失真至多为$D$。经典的Assouad嵌入定理做出了相同的断言，但是将$N\to \infty$作为$\e\to 0$。
英文摘要：
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 $\e\to 0$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
