Uniformities and covering properties for partial frames (II)
John Frith, Anneliese Schauerte
Abstract. This paper is a continuation of , in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and nite meets distribute over these. After presenting there our axiomatization of partial frames, which we call S-frames, we added structure, in the form of S-covers and nearness. Here, in the unstructured setting, we consider regularity, normality and compactness, expressing all these properties in terms of S-covers. We see that an S-frame is normal and regular if and only if the collection of all nite S-covers forms a basis for an S-uniformity on it. Various results about strong inclusions culminate in the proposition that every compact, regular S-frame has a unique compatible S-uniformity.