A non-trivial copy of 𝛽ℕ∖ℕ

There is a copy K K of the Stone-Cech remainder, β N ∖ N = N ∗ \beta \mathbb N\setminus \mathbb N = \mathbb N^* , of the integers inside N ∗ \mathbb N^* that is not equal to D ¯ ∖ D \overline {D}\setminus D for any countable discrete D ⊂ β N D\subset \beta \mathbb N . Such a copy of N ∗ \mathbb N^* is known as a non-trivial copy of N ∗ \mathbb N^* . This answers a longstanding open problem of Eric van Douwen.