关于Scott开滤子拓扑核紧性的注记

本文构造了两个例子:(1)利用康托三分集构造了一个非连续的DCPO,这个非连续DCPO关于所有Scott开滤子为子基生成的拓扑是核紧的,T0的,且以Scott开滤子为基,从而回答了[2]提出的一个问题;(2)利用Domain函数空间给出一个非连续的DCPO,其上的Scott拓扑有开滤子基,这个例子比[3]中给出的更直观.     

关于Scott拓扑存在开滤子拓扑基的分配备格

本文利用引入的ＫＳ性质,刻划了那些其Ｓｃｏｔｔ拓扑可由开滤子生成的分配备格,该结果也是对［１］中一公开问题的一种解答．本文的刻划定理对于判定分配备格的Ｓｃｏｔｔ拓扑是否与Ｓｃｏｔｔ开滤子拓扑一致具有较强的可操作性,应用该刻划定理给出大量非连续格,其Ｓｃｏｔｔ拓扑具有开滤子基．     

伪Scott拓扑与伪Scott开滤子

讨论抽象基(特别是偏序集带辅助序)上的伪Scott拓扑与伪Scott开滤子集的一些基本性质, 推广了Domain理论中一些熟知的结论,证明了抽象基上的伪Scott拓扑是完全分配格;若在偏序集P上赋予辅助关系＜, 则其上伪Scott开滤子之集是连续domain.     

Domain函数空间上的Isbell拓扑和Scott拓扑的一致性

本文主要讨论了Domain函数空间上Isbell拓扑和Scott拓扑的一致性.利用Domain函数空间给出了一个例子: Scott拓扑有开滤子基的非连续的DCPO.     

偏序集中网和滤子的Scott收敛及其Scott拓扑

本文的目的是在偏序集上直接定义和研究网和滤子的Scott收敛理论,指出其相互之间的协调性,及其它们的导出拓扑与Scott拓扑的一致性.     

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。     

不分明化拓扑中近似紧性和几乎紧性

在不分明化拓扑空间中,从正则开集出发引入了近似紧性和几乎紧性的概念,并且给出了它们的一些性质.这些概念的结合有助于我们对不分明化拓扑的研究。     

代数L-domain和强core紧空间的刻画

给出代数L-domain和强core紧空间以及连续L-domain和core紧空间的刻画。     

RL-拓扑及其紧性

本文提出了$L$-模糊子集$A$上$RL$-拓扑的概念,使得$L$-拓扑成为其特殊情形.给出了$RL$-拓扑空间之间$RL$-连续映射的定义,并利用不等式探讨了$RL$-拓扑的紧性,引入了$RL$-紧的定义,并研究了该紧性的若干性质.     

不分明化拓扑中强紧性

在不分明化拓扑空间中,从pre-开集出发引入了强紧性的概念,并且给出了它的一些性质.这些概念的结合有助于我们对不分明化拓扑的研究.     

Quasicontinuity of Posets via Scott Topology and Sobrification

In this paper, posets which may not be dcpos are considered. In terms of the Scott topology on posets, the new concept of quasicontinuous posets is introduced. Some properties and characterizations of quasicontinuous posets are examined. The main results are: (1) a poset is quasicontinuous iff the lattice of all Scott open sets is a hypercontinuous lattice; (2) the directed completions of quasicontinuous posets are quasicontinuous domains; (3) A poset is continuous iff it is quasicontinuous and meet continuous, generalizing the relevant result for dcpos. Supported by the NSF of China (10371106, 10410638) and by the Fund (S0667-082) from Nanjing University of Aeronautics and Astronautics.     

局部有限超拓扑的局部紧性

本文讨论了赋予局部有限拓扑的非空闲子集超空间的局部紧性.主要结果是:X正则,则其闭子集超空间局部紧当且仅当X可表示成一个紧空间与一个离散空间的拓扑和.     

不分明拓扑中的一种覆盖式紧性

本文利用包含度来区分覆盖的层次，提出了一种新的覆盖式不分明紧性并建立了其Ｔｙｃｈｎｏｆｆ定理．     

相容Domain间Scott连续自映射的不动点

研究相容连续L-dom a in之间的稳定映射以及相容FS-dom a in之间的一致交换映射的不动点之集的性质。     

Strongly continuous posets and the local Scott topology

In this paper, the concept of strongly continuous posets (SC-posets, for short) is introduced. A new intrinsic topology—the local Scott topology is defined and used to characterize SC-posets and weak monotone convergence spaces. Four notions of continuity on posets are compared in detail and some subtle counterexamples are constructed. Main results are: (1) A poset is an SC-poset iff its local Scott topology is equal to its Scott topology and is completely distributive iff it is a continuous precup; (2) For precups, PI-continuity, LC-continuity, SC-continuity and the usual continuity are equal, whereas they are mutually different for general posets; (3) A T₀-space is an SC-poset equipped with the Scott topology iff the space is a weak monotone convergence space with a completely distributive topology contained in the local Scott topology of the specialization order.     

Complexity spaces as quantitative domains of computation

We study domain theoretic properties of complexity spaces. Although the so-called complexity space is not a domain for the usual pointwise order, we show that, however, each pointed complexity space is an ω-continuous domain for which the complexity quasi-metric induces the Scott topology, and the supremum metric induces the Lawson topology. Hence, each pointed complexity space is both a quantifiable domain in the sense of M. Schellekens and a quantitative domain in the sense of P. Waszkiewicz, via the partial metric induced by the complexity quasi-metric.