Geodesic
Two-to-one continuous images of $\mathbb{N}^*$
Alan Dow1 ; Geta Techanie1
1 Department of Mathematics University of North Carolina at Charlotte 9201 University City Blvd. Charlotte, NC 28223-0001, U.S.A.
Fundamenta Mathematicae, Tome 186 (2005) no. 2, pp. 177-192.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm186-2-5
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

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},
     publisher = {mathdoc},
     volume = {186},
     number = {2},
     year = {2005},
     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
PY  - 2005
SP  - 177
EP  - 192
VL  - 186
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm186-2-5/
DO  - 10.4064/fm186-2-5
LA  - en
ID  - 10_4064_fm186_2_5
ER  - 
%0 Journal Article
%A Alan Dow
%A Geta Techanie
%T Two-to-one continuous images of  $\mathbb{N}^*$
%J Fundamenta Mathematicae
%D 2005
%P 177-192
%V 186
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm186-2-5/
%R 10.4064/fm186-2-5
%G en
%F 10_4064_fm186_2_5
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. http://geodesic.mathdoc.fr/articles/10.4064/fm186-2-5/

Cité par Sources :