Somewhere trivial automorphisms

TL;DR

This paper demonstrates the consistency of a non-trivial autohomeomorphism of beta N that is trivial on some open set, using a Velickovic model where Martin's Axiom also holds.

Contribution

It introduces a model where a non-trivial autohomeomorphism of beta N exists, yet all such automorphisms are trivial on some open set, combining set-theoretic and topological insights.

Findings

Existence of a non-trivial autohomeomorphism of beta N in a specific model.

All autohomeomorphisms are trivial on some open set in this model.

The model also satisfies Martin's Axiom.

Abstract

It is shown to be consistent that there is a non-trivial autohomeomorphism of beta N while all such autohomeomorphisms are trivial on some open set. The model used is one due to Velickovic in which, coincidentally, Martin's Axiom also holds.