The Katowice problem and autohomeomorphisms of $\omega^*$

TL;DR

This paper explores the implications of a homeomorphism between certain topological spaces, showing it leads to non-trivial autohomeomorphisms, thus advancing understanding of their structural properties.

Contribution

It establishes a link between the existence of a homeomorphism between  and 
spaces and the existence of non-trivial autohomeomorphisms of .

Findings

Existence of a homeomorphism implies non-trivial autohomeomorphisms.

Provides new insights into the structure of  spaces.

Advances understanding of the Katowice problem.

Abstract

We show that the existence of a homeomorphism between $\omega_0^*$ and $\omega_1^*$ entails the existence of a non-trivial autohomeomorphism of $\omega_0^*$.