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Sep 10 at 18:23 vote accept Gro-Tsen
Sep 10 at 18:23 comment added Gro-Tsen Thanks! This was exactly the explanation I needed. Both papers are quite interesting, and, crucially, I had missed the fact that when $B$ is countable it can be partitioned into countably many nonempty clopen sets. I just wrote a streamlined proof on MSE that $B$ countable implies that $\beta B$ cannot equal $\{0,1\}^S$.
Sep 10 at 9:26 history edited Gro-Tsen CC BY-SA 4.0
add label of precise theorem in each cited paper
Sep 9 at 21:20 history answered KP Hart CC BY-SA 4.0