Extending homeomorphisms on Cantor cubes

Abstract

We discuss the question of extending homeomorphism between closed subsets of the Cantor discontinuum $D^\tau$. It is established that any homeomorphism $f$ between two closed subsets of $D^\tau$ can be extended to an autohomeomorphism of $D^\tau$ provided $f$ preserves the $\lambda$-interiors of the sets for every cardinal $\lambda$.