
Recent Posts
Recent Comments
 xiaodong.jia on Wellfiltered 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
Category Archives: Uncategorized
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 nonconsonance 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 nonconsonance arguments
The space S0
S0 is a space that occurs in Matthew de Brecht’s generalized Hurewicz theorem for quasiPolish spaces, published in 2018. S0 is very simple: it is an infinite countablybranching 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 socalled 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 filterrelated monads: II. KZmonads
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 categorytheoretic construction … Continue reading
Posted in Uncategorized
Tagged algebra, continuous lattice, filter, monad
Comments Off on Algebras of filterrelated monads: II. KZmonads
Algebras of filterrelated 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/categorytheoretic of the otherwise purely topological notion of compact … Continue reading
Posted in Uncategorized
Tagged algebra, compactness, filter, monad
Comments Off on Algebras of filterrelated monads: I. Ultrafilters and Manes’ theorem
A report from ISDT’22: onestep closure; cspaces are not CCC
I have been attending the 9th International Symposium on Domain Theory (ISDT’22), which took place online, July 46, 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: onestep closure; cspaces are not CCC
Q is not consonant: the CostantiniWatson argument
I have already given an argument for the nonconsonance 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 CostantiniWatson argument