Author Archives: jgl

Forbidden substructures

Characterizing properties of graphs, posets, and even dcpos by forbidden substructures is an intriguing approach.  Xiaodong Jia managed to show that every CCC of quasi-continuous domains must consist of continuous domains exclusively, and I would like to explain how this rests … Continue reading

Posted in Uncategorized | Comments Off on Forbidden substructures

Meet-continuous spaces

Meet-continuous dcpos were defined and studied by Hui Kou, Ying-Ming Liu, and Mao-Kang Luo about 14 years ago, and their importance only starts to be appreciated now.  One of the leading results in the theory of meet-continuous dcpos is that a dcpo is continuous if … Continue reading

Posted in Uncategorized | Comments Off on Meet-continuous spaces

Markowsky or Cohn?

I have already mentioned Markowsky’s Theorem (1976): every chain-complete poset is a dcpo.  This is a non-trivial theorem, and I’ve given you a proof of it based on Iwamura’s Lemma and ordinals in a previous post.  Maurice Pouzet recently pointed … Continue reading

Posted in Uncategorized | Comments Off on Markowsky or Cohn?

Integration

At the start of the book, I had stated: “Topological convexity, topological measure theory, hyperspaces, and powerdomains will be treated in further volumes.”  The book got out in 2013, but I wrote that in 2011, almost seven years ago now.  What … Continue reading

Posted in Uncategorized | Comments Off on Integration

In memoriam: Klaus Keimel

Klaus Keimel passed away on Saturday, November 18th, 2017, and this is sad news.  I would like to pay homage to his memory, through a partial recollection of my own path with Klaus.  

Posted in Uncategorized | Comments Off on In memoriam: Klaus Keimel

A characterization of FAC spaces

In the open problem section, I defined a FAC space as a topological space in which every closed subspace is a finite union of irreducible closed subspaces. FAC is for “finite antichain property”, since it generalizes the following theorem, due … Continue reading

Posted in Uncategorized | Comments Off on A characterization of FAC spaces

Isbell’s density theorem and intersection of sublocales

When I wrote my latest blog post, there were many things I thought would be useful to know about sublocales.  Those eventually turned out to be useless in that context.  However, I think they should be known, in a more … Continue reading

Posted in Uncategorized | Tagged , | Comments Off on Isbell’s density theorem and intersection of sublocales

The O functor does not preserve binary products

In Exercise 8.4.23 of the book, I said: “Exercise 8.4.21 may give you the false impression that the O functor preserves binary products. This is wrong, although an explicit counterexample seems too complicated to study here: see Johnstone (1982, 2.14).” … Continue reading

Posted in Uncategorized | Tagged , | Comments Off on The O functor does not preserve binary products

Well-filtered dcpos

I have just returned from the International Symposium on Domain Theory, which took place in Shijiazhuang, Hebei, China.  That was a fine conference indeed.  There, I met Xiaoyong Xi and Jimmie Lawson, who just happened to publish a remarkable result, … Continue reading

Posted in Uncategorized | 1 Comment

Bounded complete and dcpo models of T1 spaces

The nice thing about colleagues is that, sometimes, they give me a primer on their latest results.  I would like to talk about a strange result by Dongsheng Zhao and Xiaoyong Xi, which, while accepted for publication, does not seem … Continue reading

Posted in Uncategorized | Comments Off on Bounded complete and dcpo models of T1 spaces