-
Recent Posts
Recent Comments
- xiaodong.jia on Well-filtered dcpos
- jordan 11 legend blue on Bourbaki, Witt, and a theorem of Dito Pataraia’s
- air jordan 11 legend blue on Bourbaki, Witt, and a theorem of Dito Pataraia’s
- jordan legend 11s on Bourbaki, Witt, and a theorem of Dito Pataraia’s
- jordan 11 legend blue 2014 on Bourbaki, Witt, and a theorem of Dito Pataraia’s
Archives
- November 2023
- October 2023
- September 2023
- August 2023
- July 2023
- June 2023
- May 2023
- April 2023
- March 2023
- February 2023
- January 2023
- December 2022
- November 2022
- October 2022
- September 2022
- August 2022
- July 2022
- June 2022
- May 2022
- April 2022
- March 2022
- February 2022
- January 2022
- December 2021
- November 2021
- October 2021
- September 2021
- August 2021
- July 2021
- June 2021
- May 2021
- April 2021
- March 2021
- February 2021
- January 2021
- December 2020
- November 2020
- October 2020
- September 2020
- August 2020
- July 2020
- June 2020
- May 2020
- April 2020
- March 2020
- February 2020
- January 2020
- December 2019
- November 2019
- October 2019
- September 2019
- August 2019
- July 2019
- June 2019
- May 2019
- April 2019
- March 2019
- February 2019
- January 2019
- December 2018
- November 2018
- October 2018
- September 2018
- August 2018
- July 2018
- June 2018
- May 2018
- April 2018
- March 2018
- February 2018
- January 2018
- December 2017
- November 2017
- October 2017
- September 2017
- July 2017
- June 2017
- April 2017
- February 2017
- January 2017
- October 2016
- August 2016
- July 2016
- June 2016
- May 2016
- April 2016
- March 2016
- January 2016
- December 2015
- October 2015
- September 2015
- July 2015
- June 2015
- May 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- September 2014
- July 2014
- June 2014
- May 2014
- March 2014
- January 2014
- December 2013
- November 2013
- October 2013
- July 2013
- June 2013
- April 2013
- February 2013
- October 2012
Meta
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 frame, locale
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 frame, locale
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