-
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
Localic products and Till Plewe’s game
Products in the category of locales resemble, but do not coincide with products in the category of topological spaces. Till Plewe has a nice explanation to this, as I will explain in this month’s post: the localic product of two … Continue reading
Posted in Uncategorized
Tagged consonance, counterexample, frame, game, locale, ordinal
Comments Off on Localic products and Till Plewe’s game
On Till Plewe’s game and Matthew de Brecht’s non-consonance arguments
Last time I mentioned that S0 is not consonant. I will give Matthew de Brecht’s proof of that. Perhaps the most interesting part of this proof is a criterion that he proves and uses: if a space X is consonant, … Continue reading
Posted in Uncategorized
Tagged consonance, counterexample, game, ordinal
Comments Off on On Till Plewe’s game and Matthew de Brecht’s non-consonance arguments
The space S0
S0 is a space that occurs in Matthew de Brecht’s generalized Hurewicz theorem for quasi-Polish spaces, published in 2018. S0 is very simple: it is an infinite countably-branching tree, and if you order it so that the root is at … Continue reading
Aliaume Lopez’ master theorem of Noetherian spaces
There are quite a few constructions that we can use to build new Noetherian spaces from old ones: spaces of finite words, of finite trees (as in Section 9.7 of the book), and a few others. Instead of writing a new … Continue reading
Posted in Uncategorized
Tagged noetherian, ordinal, wqo
Comments Off on Aliaume Lopez’ master theorem of Noetherian spaces
Weakly Hausdorff spaces, and locally strongly sober spaces
A funny convergence of topics happened a few weeks ago. Frédéric Mynard told me about so-called locally strongly sober spaces (which, I am ashamed to say, I had heard about but completely forgotten about). At the same time, I was … Continue reading
Posted in Uncategorized
Tagged filters
Comments Off on Weakly Hausdorff spaces, and locally strongly sober spaces
Strongly compact sets and the double hyperspace construction
The notion of strongly compact set is due to Reinhold Heckmann. A few months ago, I said that I would explain why the sobrification of the space Qfin(X) of finitary compact sets on a sober space X is not the … Continue reading
Posted in Uncategorized
Tagged compactness, hyperspace, powerdomain
Comments Off on Strongly compact sets and the double hyperspace construction
Algebras of filter-related monads: II. KZ-monads
Alan Day and Oswald Wyler once proved that the algebras of the filter monad on the category Top0 of T0 topological spaces are exactly the continuous (complete) lattices. Martín Escardó later gave a very interesting proof of this fact, using a category-theoretic construction … Continue reading
Posted in Uncategorized
Tagged algebra, continuous lattice, filter, monad
Comments Off on Algebras of filter-related monads: II. KZ-monads
Algebras of filter-related monads: I. Ultrafilters and Manes’ theorem
In 1969, Ernest Manes proved the following remarkable result: the algebras of the ultrafilter monad on Set are exactly the compact Hausdorff spaces. This is remarkable, because it gives a purely algebraic/category-theoretic of the otherwise purely topological notion of compact … Continue reading
Posted in Uncategorized
Tagged algebra, compactness, filter, monad
Comments Off on Algebras of filter-related monads: I. Ultrafilters and Manes’ theorem
A report from ISDT’22: one-step closure; c-spaces are not CCC
I have been attending the 9th International Symposium on Domain Theory (ISDT’22), which took place online, July 4-6, 2022, in Singapore. This was a fine conference indeed, and it ran very smoothly. I initially intended to give a summary of … Continue reading
Posted in Uncategorized
Tagged cartesian closeness, closure, exponentiability
Comments Off on A report from ISDT’22: one-step closure; c-spaces are not CCC
Q is not consonant: the Costantini-Watson argument
I have already given an argument for the non-consonance of the Sorgenfrey line Rℓ here. I would now like to explain why the space Q of rational numbers is not consonant either. That is quite a challenge. The most easily … Continue reading
Posted in Uncategorized
Tagged compact, consonance, counterexample, game, scattered
Comments Off on Q is not consonant: the Costantini-Watson argument