Lev Birbrair, Alexandre Fernandes, Zbigniew Jelonek
Let X be a closed semialgebraic set of dimension k. If n≥2k+1, then there is a bi-Lipschitz and semialgebraic embedding of X into Rn. Moreover, if n≥2k+2, then this embedding is unique (up to a bi-Lipschitz and semialgebraic homeomorphism of Rn). We also give local and complex algebraic counterparts of these results.
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