-
Recent Comments
-
Archives
- October 2024
- September 2024
- August 2024
- July 2024
- June 2024
- May 2024
- April 2024
- March 2024
- February 2024
- January 2024
- December 2023
- 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
Tag Archives: sober space
Zhao, Xi and Chen’s well-filtered, non-sober dcpo
There are several known examples of dcpos that are well-filtered, but not sober, and I have already mentioned one due to Xiaodong Jia. I would like to explain another one, due to Dongsheng Zhao, Xiaoyong Xi, and Yixiang Chen. This … Continue reading
Posted in Uncategorized
Tagged counterexample, sober space, well-filtered space
Comments Off on Zhao, Xi and Chen’s well-filtered, non-sober dcpo
X. Jia’s well-filtered, non-sober dcpo
[Business as usual, despite all viruses!] Peter Johnstone once showed the existence of a dcpo J that is not sober in its Scott topology. That dcpo is not well-filtered either. Is there a dcpo that is not sober but is … Continue reading
Posted in Uncategorized
Tagged counterexample, sober space, well-filtered space
Comments Off on X. Jia’s well-filtered, non-sober dcpo
Core-compact+well-filtered T0=sober locally compact
Last time, I motivated the construction of the well-filterification Wf(X) of a space X of X. Xu, Ch. Shen, X. Xi and D. Zhao by saying that it was needed to understand their proof of the fact that every core-compact … Continue reading
Posted in Uncategorized
Tagged core-compactness, sober space, well-filtered space
Comments Off on Core-compact+well-filtered T0=sober locally compact
Sober subspaces and the Skula topology
It often happens that one wishes to show that a certain subspace A of a given sober space X is sober. The following is a pearl due to Keimel and Lawson, which was mentioned to me by Zhenchao Lyu in … Continue reading
Posted in Uncategorized
Tagged skula topology, sober space
Comments Off on Sober subspaces and the Skula topology
Shimrat’s theorem
Marcus Tressl just found a horrible mistake in the book: I had claimed that the T0 quotient of the topological quotient of any sober space by any equivalence relation is sober, but that is completely wrong. In fact, Moshe Shimrat … Continue reading
Posted in Uncategorized
Tagged Hausdorff space, quotient, sober space
Comments Off on Shimrat’s theorem