Homeomorphisms of Cech-Stone remainders: the zero-dimensional case

TL;DR

This paper demonstrates that under a weakened Proper Forcing Axiom, any homeomorphism between Cech-Stone remainders of zero-dimensional Polish spaces arises from a homeomorphism of their cocompact subspaces, revealing structural connections.

Contribution

It establishes a link between homeomorphisms of Cech-Stone remainders and homeomorphisms of cocompact subspaces in the zero-dimensional case using set-theoretic assumptions.

Findings

Homeomorphisms of Cech-Stone remainders are induced by cocompact subspace homeomorphisms.

Weakening of Proper Forcing Axiom suffices for the main result.

Structural characterization of zero-dimensional Cech-Stone remainders.

Abstract

We prove, using a weakening of the Proper Forcing Axiom, that any homemomorphism between Cech--Stone remainders of any two locally compact, zero-dimensional Polish spaces is induced by a homeomorphism between their cocompact subspaces.