Timeline for Does any subset of $\beta\omega$ of cardinality $\mathfrak{c}$ have a weak P-point in its closure?

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May 6, 2018 at 15:04	comment	added	Mathieu Baillif		Thanks for this idea. I was thinking of building such an example by induction, starting with a function $f:\omega\to[0,1]$ with a dense image, extend it to all of $\beta\omega$, pick one guy in the preimage of each point. This defines $X_0$. To go from $X_\alpha$ to $X_{\alpha+1}$, choose one point in the closure of each countable set of $X_\alpha$ (if it does not already have one in $X_\alpha$). If $\alpha$ is limit, take the union of the $X_\beta$ below it. Then $X_{\omega_1}$ is countably compact and of cardinality $\mathfrak{c}$. But your example is even better.
May 6, 2018 at 14:43	history	answered	Anonymous	CC BY-SA 4.0