TITLE: Stone Cech compactification of the naturals a cts image of the Cantor set?
QUESTION [7 upvotes]: Is $\beta \mathbb{N}$, the Stone-Cech compactification of $\mathbb{N}$, a continuous image of the Cantor set?

REPLY [10 votes]: A Hausdorff space is the continuous image of the Cantor set iff it is compact metrisable.