We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a similar result holds if we consider groups of polynomial automorphisms of affine spaces instead of Cremona groups.

中文翻译：

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Cremona 群的连续自同构

我们证明，如果任意秩的 Cremona 群的群自同构也是关于 Zariski 或欧几里得拓扑的同胚，那么它是基域的域自同构。此外，我们表明，如果我们考虑仿射空间的多项式自同构群而不是 Cremona 群，则可以得到类似的结果。