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 topological spaces coincides with their topological products if and only if player II has a winning strategy in a certain game, which I have already described last month. As a consequence, we will obtain that the localic product of S_{0} with itself is not its topological product (a result due to Matthew de Brecht), we will retrieve that the localic product of Q and of R–Q differs from their topological product (and more generally, a result of John Isbell’s), and finally that the localic product of Q with itself differs from the topological product, and that Q is not consonant… with a much, much simpler proof than those I have ever mentioned here. The idea of that argument is due to Matthew de Brecht. Read the full post.

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