The Katowice problem and autohomeomorphisms of $\ddot{I}{‰}^{\ast }$

Abstract

We show that the existence of a homeomorphism between $\ddot{I}{‰}_0^{\ast }$ and $\ddot{I}{‰}_1^{\ast }$ entails the existence of a non-trivial autohomeomorphism of $\ddot{I}{‰}_0^{\ast }$.