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 $\lambda$.

17 pages. arXiv admin note: substantial text overlap with arXiv:2109.07214

References in corpus (1)

• On homogeneity of Cantor cubes