In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite \'etale after reduction. When $k$ is a real closed field, we prove that such a morphism induces a covering map on the rational points.

翻译：本文证明，对于特征为零的域$k$上具有局部常值几何纤维的平坦$k$-簇态射，经约化后可成为有限平展态射。当$k$为实闭域时，我们证明此类态射在其有理点集上诱导覆盖映射。