Lawvere Completeness in Topology

摘要: It is known since 1973 that Lawvere’s notion of Cauchy-complete enriched category meaningful for metric spaces: it captures exactly spaces. In this paper, we introduce the corresponding Lawvere completeness $(\mathbb{T},\mathsf{V})$ -categories and show has an interesting meaning topological spaces quasi-uniform former ones means weak sobriety while latter Cauchy completeness. Further, $\mathsf{V}$ a canonical -category structure which plays key role: Lawvere-complete under reasonable conditions on setting; permits us to define Yoneda embedding in realm -categories.