On countability: the compact completed sequence

Recently, Matthew de Brecht sent me a proof of a neat and rather surprising result: the product and the Scott topologies coincide for products of first-countable, not necessarily continuous, posets. This rests on a clever argument, inspired by techniques invented by Matthias Schröder, and a simple observation: if you take all the elements of a convergent sequence, plus one (any) of its limits, what you get is a compact set. The latter fails if you take a net instead of a sequence. Read the full post.