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.
Keywords:
function two to one every point image has exactly inverse points every two to one continuous image mathbb * homeomorphic mathbb * continuum hypothesis assumed prove there irreducible two to one continuous function whose domain mathbb * under assumption
Affiliations des auteurs :
Alan Dow
1
;
Geta Techanie
1
1
Department of Mathematics University of North Carolina at Charlotte 9201 University City Blvd. Charlotte, NC 28223-0001, U.S.A.
@article{10_4064_fm186_2_5,
author = {Alan Dow and Geta Techanie},
title = {Two-to-one continuous images of $\mathbb{N}^*$},
journal = {Fundamenta Mathematicae},
pages = {177--192},
year = {2005},
volume = {186},
number = {2},
doi = {10.4064/fm186-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm186-2-5/}
}
TY - JOUR
AU - Alan Dow
AU - Geta Techanie
TI - Two-to-one continuous images of $\mathbb{N}^*$
JO - Fundamenta Mathematicae
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VL - 186
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UR - http://geodesic.mathdoc.fr/articles/10.4064/fm186-2-5/
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%J Fundamenta Mathematicae
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Alan Dow; Geta Techanie. Two-to-one continuous images of $\mathbb{N}^*$. Fundamenta Mathematicae, Tome 186 (2005) no. 2, pp. 177-192. doi: 10.4064/fm186-2-5
