While a topological space is a space of points, a hyperspace is a space of subsets, with a suitable topology. Examples abound in the literature. For example, the so-called Smyth powerdomain (Proposition 8.3.25) is one. To start the series, let me look at the Hoare hyperspace instead. We shall see that it is a space that has many nice properties. I won’t say to which purpose it has been put in denotational semantics yet, or that it defines a monad with a very natural inequational theory… all that will have to wait! Read the full post.