Hyperspaces and powerdomains I: closed and open sets

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.