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 ℕ* is homeomorphic to ℕ* when the continuum hypothesis is assumed. We also prove that there is no irreducible two-to-one continuous function whose domain is ℕ* under the same assumption.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-2-5,
author = {Alan Dow and Geta Techanie},
title = {Two-to-one continuous images of $\mathbb{N}$*},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {177-192},
zbl = {1078.54012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-2-5}
}
Alan Dow; Geta Techanie. Two-to-one continuous images of ℕ*. Fundamenta Mathematicae, Tome 185 (2005) pp. 177-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-2-5/