On algebraic bi-Lipschitz homeomorphisms

Let $X\subset {\mathbb{C}}^n;Y\subset {\mathbb{C}}^m$ be closed affine varieties and let $\varphi :X\to Y$ be an algebraic bi-Lipschitz homeomorphism. Then ${\rm deg}\ X={\rm deg}\ Y.$Similarly,let$(X,0)\subset ($\mathbb{C}$^n,0), (Y,0)\subset ($\mathbb{C}$^m,0)$begermsofanalyticsetsandlet$f: (X,0)\to (Y,0)$beac-holomorphicandbi-Lipschitzmapping\mathrm{.}Then${\rm mult}_0 \ X= {\rm mult }_0 \ Y.$ Finally we show that the normality is not a bi-Lipschitz invariant.