  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.

Algebraic Geometry;Group Theory