Notes on paracompact coreflections of frames (Q2705852)

The scope of this paper is broader than its title indicates. In the first place, it is concerned not just with frames but with \(\kappa\)-frames (that is, the analogue of frames in which one demands only the existence and preservation of joins of cardinality at most \(\kappa\)), and secondly it considers not only the paracompact coreflection but also the compact regular and Lindelöf coreflections. The main aim of the paper is to give a `uniform' construction of the three coreflections using direct limits; the author also gives some dimension-theoretic results related to the compact and Lindelöf coreflections.