Tag Archives: sobriety

Hoover’s maximal limit spaces II: products, liftings, retracts, function spaces, and hyperspaces

Posted on April 20, 2024 by jgl

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 , , , , , , , | 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

Posted on March 20, 2024 by jgl

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 , , , , , | 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

Posted on November 20, 2022 by jgl

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 , , , , , | Comments Off on Weakly Hausdorff spaces, and locally strongly sober spaces