as the title says. Let $A^n$ be an $n$-dimensional closed Alexandrov space. Does it admit a bi-Lipschitz embedding into the Euclidiean space $\mathbb R^N$ for sufficiently large $N$?
I know there are some spaces does not admit such embedding, for example a theorem by Pansu says that:
The Heisenberg group equipped with the Carnot-Caratheodory distance does not biLipschitz embed into $\mathbb R^n$, for any $n$.