@article { author = {Frith, John and Schauerte, Anneliese}, title = {Uniformities and covering properties for partial frames (II)}, journal = {Categories and General Algebraic Structures with Applications}, volume = {2}, number = {1}, pages = {23-35}, year = {2014}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {}, abstract = {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.}, keywords = {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}, url = {https://cgasa.sbu.ac.ir/article_6798.html}, eprint = {https://cgasa.sbu.ac.ir/article_6798_057cf0f670e3ade0581219ba00d22a0b.pdf} }