Uniformities and covering properties for partial frames (II)

This paper is a continuation of [uniformities and covering properties for partial frames (i)], 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 finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in the form of $sels$-covers and nearness. here, in the unstructured setting, we consider regularity, normality and compactness, expressing all these properties in terms of $sels$-covers. we see that an $sels$-frame is normal and regular if and only if the collection of all finite $sels$-covers forms a basis for an $sels$-uniformity on it. various results about strong inclusions culminate in the proposition that every compact, regular $sels$-frame has a unique compatible $sels$-uniformity.