-
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: coherence
Compact closed subsets in the patch topology
Given a coherent, well-filtered space X, one can give a pretty explicit description of the compact closed sets in Xpatch, the space obtained by equipping X with its patch topology—and we do not need local compactness or compactness. They are … Continue reading
Posted in Uncategorized
Tagged coherence, compactness, counterexample, patch topology, well-filtered space
Comments Off on Compact closed subsets in the patch topology
Hoover’s maximal limit spaces II: products, liftings, retracts, function spaces, and hyperspaces
Last time, we had introduced Hoover’s maximal limit spaces: spaces in which every convergent filter has a unique largest limit. That notion is closed under many constructions, as we will see: products, liftings, retracts, notably, and that is elementary. The … Continue reading
Posted in Uncategorized
Tagged coherence, convergence, filters, function space, hyperspace, sobriety, strong sobriety, weak Hausdorffness
Comments Off on Hoover’s maximal limit spaces II: products, liftings, retracts, function spaces, and hyperspaces
Hoover’s maximal limit spaces I: local strong sobriety, bounded sup-completeness and weak Hausdorffness
In 1995, Douglas Hoover introduced and studied a notion of maximal limit spaces: spaces in which every convergent net has a unique largest limit. This has connections with many other kinds of spaces that we have explored already, and I … Continue reading
Posted in Uncategorized
Tagged coherence, convergence, filters, sobriety, strong sobriety, weak Hausdorffness
Comments Off on Hoover’s maximal limit spaces I: local strong sobriety, bounded sup-completeness and weak Hausdorffness
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 coherence, convergence, filters, sobriety, strong sobriety, weak Hausdorffness
Comments Off on Weakly Hausdorff spaces, and locally strongly sober spaces