\(T_ 1\) spaces over topological sites
This brief note provides an elegant way of showing that in topological toposes many spaces can be represented as sheaves of continuous functions into the appropriate formal space. A locale X is called \(T_ 1\) iff for all locale morphisms f,g: \(Y\to X\), \(f^*\leq g^*\) pointwise implies \(f=g.\) Let \({\mathcal E}\) be a topological topos, that is to say \({\mathcal E}\) is sheaves on a topological site C. Then, if X is a \(T_ 1\)-locale, the sheaf of X-models in \({\mathcal E}\) is represented by the sheaf \(Cts( ,X): C^{op}\to Sets\) of continuous X-valued morphisms.
scientific article; zbMATH DE number 3865535