On homogeneity of $\mathbb N^τ$
It is shown that any homeomorphism between two compact subsets of $\mathbb N^τ$ can be extended to an autohomeomorphism of $\mathbb N^τ$.
math.GN↗
arXiv subjects
E. Shchepin
Publications and source records attributed to E. Shchepin.
On homogeneity of Cantor cubes
It is established that any homeomorphism between two closed negligible subset of $D^τ$ can be extended to an autohomeomorphism of $D^τ$.
math.GN↗
Extending homeomorphisms on Cantor cubes
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 $\lambda$.
math.GN↗