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 space of continuous functions from a core-compact space to a maximal limit space is also a maximal limit space, as shown by Hoover. That is a more difficult theorem, which will rely on the characterizations we saw last time of maximal limit spaces as weakly Hausdorff spaces with some additional properties. We will also look at the Smyth and Hoare hyperspaces. Read the full post.