Non-trivial copies of N*

Abstract

We show that it is consistent to have regular closed non-clopen copies of ${\mathbb{N}}^{\ast }$ within ${\mathbb{N}}^{\ast }$ and a non-trivial self-map of ${\mathbb{N}}^{\ast }$ even if all autohomeomorphisms of ${\mathbb{N}}^{\ast }$ are trivial.