# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Two-to-one continuous images of $\mathbb{N}^*$

### Tom 186 / 2005

Fundamenta Mathematicae 186 (2005), 177-192 MSC: Primary 54A35, 54C10. DOI: 10.4064/fm186-2-5

#### Streszczenie

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.

#### Autorzy

• Alan DowDepartment of Mathematics
University of North Carolina at Charlotte
9201 University City Blvd.
Charlotte, NC 28223-0001, U.S.A.
e-mail
• Geta TechanieDepartment of Mathematics
University of North Carolina at Charlotte
9201 University City Blvd.
Charlotte, NC 28223-0001, U.S.A.
e-mail

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