Geodesic
Two-to-one continuous images of $\mathbb{N}^*$
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.
Fundamenta Mathematicae, Tome 186 (2005) no. 2, pp. 177-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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. 
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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

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