Sequential compactness and the splitting number

In talking with people in #scala earlier I ended up looking through some of my old maths articles. In particular this one. I noticed that I mentioned “So far the only counterexampe I have depends on the value of the reaping number, tau. It’s fairly standard (I’ll write a post on it at some point) that {0, 1}^{tau} is not sequentially compact”.

The details of the above are wrong: Firstly, I meant the splitting number rather than the reaping number (a post I found elsewhere on the internet confirms I was confusing the two – I’m not even sure what the reaping number actually is). Secondly, “fairly standard” my ass. I couldn’t find anything on it, so had to recreate it from scratch. I mean, it’s not a new result and there have been papers on it, but it’s not by any means a commonly reproduced proof. I have no access to maths journals in order to check out the original papers, and hence there will be a deplorable lack of citations here. Sorry.

Still, four years later, here’s that post. I’ve written it up as a pdf rather than subjecting you to embedded LaTeX in the post.

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