Two-to-one continuous images of $\mathbb{N}^*$
Volume 186 / 2005
Fundamenta Mathematicae 186 (2005), 177-192
MSC: Primary 54A35, 54C10.
DOI: 10.4064/fm186-2-5
Abstract
A function is two-to-one if every point in the image has exactly two inverse points. We show that every two-to-one continuous image of $\mathbb{N}^*$ is homeomorphic to $\mathbb{N}^*$ when the continuum hypothesis is assumed. We also prove that there is no irreducible two-to-one continuous function whose domain is $\mathbb{N}^*$ under the same assumption.
