Uniformities and covering properties for partial frames (II)

Categories and General Algebraic Structures with Applications

Anneliese Schauerte¹  John Frith¹ 

[1] Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch, 7701, South Africa.;

关键词: 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;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown