On homogeneity of Cantor cubes

TL;DR

This paper proves that any homeomorphism between two small, negligible closed subsets of a Cantor cube can be extended to an autohomeomorphism of the entire cube, highlighting a significant extension property.

Contribution

It establishes a new extension property for homeomorphisms between negligible closed subsets of Cantor cubes, advancing understanding of their topological structure.

Findings

Homeomorphisms between negligible closed subsets extend to autohomeomorphisms.

Extension property holds for arbitrary Cantor cubes.

Enhances understanding of the topological symmetry of Cantor cubes.

Abstract

It is established that any homeomorphism between two closed negligible subset of $D^\tau$ can be extended to an autohomeomorphism of $D^\tau$.