论文标题
佩尔文空间的无点理论
A pointfree theory of Pervin spaces
论文作者
论文摘要
我们为Pervin空间的无点理论奠定了基础。 Pervin空间是配备了其PowerSet的有界sublattice的集合，众所周知，这些对象表征了那些及时且完全界限的准均匀空间。我们称为Frith框架的Pervin空间的无点概念由配备有生成有限的Sublattice的框架组成。在本文中，我们介绍并研究了Frith框架的类别，并表明拓扑空间和框架之间的经典双重辅助延伸至Pervin空间和Frith框架之间的双重辅助。与Pervin空间发生的情况不同，我们在及时的和完全有限的准均匀框架和Frith框架之间没有等效性，但是我们表明后者是前者的完整核心式子类别。我们还探讨了从准均匀框架继承的Frith框架的完整性概念，从而对那些完整的Frith框架进行了表征，并描述了任意Frith框架的完成。
We lay down the foundations for a pointfree theory of Pervin spaces. A Pervin space is a set equipped with a bounded sublattice of its powerset, and it is known that these objects characterize those quasi-uniform spaces that are transitive and totally bounded. The pointfree notion of a Pervin space, which we call Frith frame, consists of a frame equipped with a generating bounded sublattice. In this paper we introduce and study the category of Frith frames and show that the classical dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames. Unlike what happens for Pervin spaces, we do not have an equivalence between the categories of transitive and totally bounded quasi-uniform frames and of Frith frames, but we show that the latter is a full coreflective subcategory of the former. We also explore the notion of completeness of Frith frames inherited from quasi-uniform frames, providing a characterization of those Frith frames that are complete and a description of the completion of an arbitrary Frith frame.
