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.

کلیدواژه ها:

frame ، sels-frame ، Z-frame ، partial frame ، sigma-frame ، kappa-frame ، meet-semilattice ، nearness ، Uniformity ، strong inclusion ، uniform map ، coreflection ، P-approximation ، strong ، totally bounded ، regular ، normal ، compact