Let $\beta(\mathbb{N})$ denote the Stone-Cech compatification of the natural numbers and $\beta(\mathbb{N})\setminus\mathbb{N}$ denote the reminder of this compactification. I wonder if there is a characterization in ZFC of the continuous images of $\beta(\mathbb{N})\setminus\mathbb{N}$. I mean: Which compact Hausdorff spaces are continuous images of $\beta(\mathbb{N})\setminus\mathbb{N}$?

Let $\beta \mathbb{N}$ denote the Stone-Cech compatification of the natural numbers and $\beta \mathbb{N} \setminus\mathbb{N}$ denote the reminder of this compactification. I wonder if there is a characterization in ZFC of the continuous images of $\beta \mathbb{N} \setminus\mathbb{N}$. I mean: Which compact Hausdorff spaces are continuous images of $\beta \mathbb{N} \setminus\mathbb{N}$?

Let betaN denote the Stone-Cech compatification of the natural numbers and betaN\N denote the reminder of this compactification. I wonder if there is a characterization in ZFC of the continuous images of beta N\N. I mean: Which compact Hausdorff spaces are continuous images of betaN\N?

Let $\beta(\mathbb{N})$ denote the Stone-Cech compatification of the natural numbers and $\beta(\mathbb{N})\setminus\mathbb{N}$ denote the reminder of this compactification. I wonder if there is a characterization in ZFC of the continuous images of $\beta(\mathbb{N})\setminus\mathbb{N}$. I mean: Which compact Hausdorff spaces are continuous images of $\beta(\mathbb{N})\setminus\mathbb{N}$?