拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

无点滤子收敛

我们在ｌｏｃａｌｅ上定义了一种新的滤子收敛概念．对空间式ｌｏｃａｌｅ,这种收敛与拓扑收敛等价,并且适应于任意ｌｏｃａｌｅ．作为应用,我们给出了ｌｏｃａｌｅ紧的程度的刻划和 Ｃａｕｃｈｙ完备性的描述．     

一致Locale的乘积

本文利用Ｌｏｃａｌｅ上的收敛结构研究一致Ｌｏｃａｌｅ的乘积结构，证明了一致Ｌｏ ｃａｌｅ的完备性关于Ｌｏｃａｌｅ积和弱积封闭．     

Locale的函数空间

构造性地定义了Locale间的Isbell,紧开及点态函数空间,研究了其良好的范畴性质(Proper和Admissible性质)及分离性质.重新得到了有指数Locale的结构.这些工作是寻找Locale范畴中的方便范畴的基础.     

Locale的函数空间

构造性地定义了Locale间的Isbell,紧开及点态函数空间,研究了其良好的范畴性质(Proper和Admissible性质)及分离性质.重新得到了有指数Locale的结构.这些工作是寻找Locale范畴中的方便范畴的基础。     

Representation Theorems for Quantales

In this paper we prove that any quantale Q is (isomorphic to) a quantale of suitable relations on Q. As a consequence two isomorphism theorems are also shown with suitable sets of functions of Q into Q. These theorems are the mathematical background one needs in order to give natural and complete semantics for (non-commutative) Linear Logic using relations. Mathematics Subject Classification: 06D05, 06D10, 06D20, 03G25.     

On some peculiar aspects of the constructive theory of point‐free spaces

This paper presents several independence results concerning the topos‐valid and the intuitionistic (generalised) predicative theory of locales. In particular, certain consequences of the consistency of a general form of Troelstra's uniformity principle with constructive set theory and type theory are examined (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strongly Zero-Dimensional Locales

New kinds of strongly zero-dimensional locales are introduced and characterized, which are different from Johnstone's, and almost all the topological properties for strongly zero-dimensional spaces have the pointless localic forms. Particularly, the Stone-Čech compactification of a strongly zero-dimensional locale is strongly zero-dimensional. Received January 21, 1999, Accepted February 1, 2000     

Locale的弱拓扑表达

本文引入了弱拓扑空间的概念,证明了locale范畴与弱拓扑空间范畴的关系类似于拓扑空间范畴与locale范畴的关系。locale范畴严格包含于弱拓扑空间范畴并且与Sober的弱拓扑空间范畴等价。