On countability

Let me first wish you a Merry Christmas, and since I will not post again next week, a Happy New Year 2019 as well.  I have no specific present this year, sorry… This month’s post is about a few thoughts I have had about the role of countability is a few situations other than the expected ones.  This will culminate in a recent result of de Brecht and Kawai—the Scott and the upper Vietoris topologies coincide on the Smyth powerdomain of a well-filtered second-countable space— and its clever proof: see the full post.