A non-trivial copy of 𝛽ℕ∖ℕ

Dow, Alan

doi:10.1090/S0002-9939-2014-11985-X

A non-trivial copy of $\beta \mathbb N\setminus \mathbb N$
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Proc. Amer. Math. Soc. 142 (2014), 2907-2913 Request permission

Abstract:

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

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