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Apr 2, 2022 at 19:28 comment added Sam Sanders With the gift of hindsight, I now see how an alternative proof would go: one generalises HBU to coverings of RM-closed sets and then applies the ECF translation. Here, HBU expresses that for $\Psi: [0,1]\rightarrow \mathbb{R}^+$, there are $x_0, ..., x_k$ such that $\cup_{i\leq k} B(x_i, \Psi(x_i))$ covers $[0,1]$.
Mar 29, 2022 at 10:03 comment added Emil Jeřábek You're welcome.
Mar 29, 2022 at 8:37 comment added Sam Sanders Thanks for the nice answer!
Mar 29, 2022 at 8:37 vote accept Sam Sanders
Mar 28, 2022 at 13:51 history answered Emil Jeřábek CC BY-SA 4.0