Abstract
Let X be a closed semialgebraic set of dimension k. If \(n\ge 2k+1\), then there is a bi-Lipschitz and semialgebraic embedding of X into \(\mathbb {R}^n\). Moreover, if \(n \ge 2k+2\), then this embedding is unique (up to a bi-Lipschitz and semialgebraic homeomorphism of \(\mathbb {R}^n\)). We also give local and complex algebraic counterparts of these results.
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