Uniformities and covering properties for partial frames (II)
Author(s):
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 , σ-frame , κ-frame , meet-semilattice , nearness , uniformity , strong inclusion , uniform map , coreflection , P-approximation , strong , totally bounded , regular , Normal , compact
Language:
English
Published:
Categories and General Algebraic Structures with Applications, Volume:2 Issue: 1, Jul 2014
Pages:
23 to 35
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