Category Archives: Uncategorized

We know a lot of Stone-like dualities, and I would like to start exploring a form of Stone duality for preordered topological spaces. We start with a simple problem this month: duality for preordered sets; hence, no topology (yet) in … Continue reading →

In 1993, Knijnenburg studied lenses, and came up with a simple dcpo that shows that the topological and the ordinary Egli-Milner orderings on lenses can differ. This dcpo settles more than this question. For example, it is an algebraic dcpo … Continue reading →

We continue our study of the class of compactly Choquet-complete spaces. We will show two things. First, that this class is closed under finite and countable products, but not under arbitrary products. While the technique for finite products consists in … Continue reading →

A completely Baire space is a space that is not only Baire, but whose closed subspaces are all Baire. We will continue our exploration of compactly Choquet-complete spaces, and we will see that they are all completely Baire. In fact, … Continue reading →

A Choquet-complete space is one in which player α has a winning strategy in the strong Choquet game. By winning, it is meant that the intersection of all the open sets played by α is non-empty. If you change the … Continue reading →

We will see a relatively recent theorem of Jimmie Lawson’s: consider a locally compact space X with a semiclosed ordering ≤, and a closed connected chain C inside X; then every closed interval inside C is compact in X. The … Continue reading →