Locales, sublocales II: sieves

Last time, I promised you we would explore another way of defining sublocales.  We shall again use the naive approach that consists in imagining how we would encode subspaces of a T0 topological space X by looking at open subsets only, and certainly not at points.  We shall encode a localic version of the notion of subspaces through what I call sieves, which are certain sets of formal crescents.  I’ll then show you that this gives you a complete lattice that is isomorphic to the lattice of sublocales that we have seen last time.  See the full post.