Author Archives: jgl

Johnstone space J (1981) is the most famous example of a non-sober dcpo. In 1982, Isbell came up with a non-sober complete lattice. His construction is so complex that most authors use it as a black box. I would like … Continue reading →

Last time, I had announced that we would do Exercise V-5.25 of the red book, constructing a core-compact, yet not locally compact, space.  And this is exactly what we shall do: read the full post.

This month, we will start to do Exercise V-5.25 of the red book (Continuous Lattices and Domains), which gives an example of a core-compact, not locally compact space.  That is pretty hard to obtain, really.  This month, we will do … Continue reading →

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 … Continue reading →

Last time, we embarked on proving that the projective limit of a projective system of compact sober (resp., and non-empty) spaces is compact and sober (resp., and non-empty), a theorem that Fujiwara and Kato call Steenrod’s Theorem.  However, instead, we … Continue reading →

Last time, I explained some of the strange things that happen with projective limits of topological spaces: they can be empty, even if all the spaces in the given projective system are non-empty and all bonding maps are surjective, and … Continue reading →

This month, let me investigate projective limits of topological spaces.  That is an area of mathematics that is fraught with pitfalls, and I will describe a number of odd situations that can occur in that domain.  You will have to … Continue reading →

I thought I would devote my blog this month to the Domains workshop, but a sudden health problem prevented me to go there.  Instead, I will talk about a curious alternative to Stone duality, which, instead of an adjunction between Top … Continue reading →