笛卡儿闭Domain范畴的两个重要性质

对于CONT的任意一个笛卡儿闭的满子范畴C,构造CONT的两个新的满子范畴R-C(以C对象的收缩为对象的范畴)和B-C(以C扩张序列的双极限为对象的范畴),并证明了它们都是笛卡儿闭范畴。由于R-C和B-C都包含C为其满子范畴,利用上述结果可得CONT的极大笛卡儿闭子范畴必对收缩和双极限封闭。本文还从范畴笛卡儿闭性的角度给出了Domain理论中一个公开问题的等价描述。     

Generalization for Amann's and Leggett-Williams' three-solution theorems and applications

In this paper, some new three-solution theorems are obtained. Moreover, the famous Amann's and Leggett-Williams' three-solution theorems in nonlinear functional analysis can be seen as their special cases, namely these two famous theorems are united. So they are both improved. And that some new three-solution theorems are applied to ordinary differential equations, and some new existence results are obtained.     

2-弱幂P(△)-半群

本文刻划了半格不可分的＞－弱幂ｐ－半群，描述了半格可分的２－弱幂ｐ－半群的结构．在此基础上，刻划了２－弱幂△－半群．     

Retracts in Polydisk and Analytic Varieties with the <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>-Extension Property

This article mainly concerns retracts in polydisk, analytic varieties with the H ^∞-extension property and the three-point Pick problem on . Arising in the study of Nevanlinna-Pick interpolation on the bidisk, Agler and McCarthy recently discovered a remarkable theorem which characterizes subsets in the bidisk with the polynomial extension property, and in this case, these subsets are retracts. To study H ^∞-extensions of holomorphic functions from subvarieties of polydisk, one naturally is concerned with retracts in polydisk. Under certain mild assumptions, it is shown that subvarieties with H ^∞-extension property are exactly retracts. Furthermore, we apply our argument to determine those retracts whose retractions are unique. In particular, a retract in having at least two different retractions is exactly a balanced disk. As an application, we give a sufficient condition of the uniqueness of the solution for the three-point Pick problem on .      

Netlike partial cubes II. Retracts and netlike subgraphs

First we show that the class of netlike partial cubes is closed under retracts. Then we prove, for a subgraph G of a netlike partial cube H, the equivalence of the assertions: G is a netlike subgraph of H; G is a hom-retract of H; G is a retract of H. Finally we show that a non-trivial netlike partial cube G, which is a retract of some bipartite graph H, is also a hom-retract of H if and only if G contains at most one convex cycle of length greater than 4.     

强可收缩半群

设S为半群 ,H为S的子半群 ,称H是S的一个缩回 ,若存在满同态 φ :S→H满足 φ｜H =1H(H上的恒等映射 ) ,称半群S是强可收缩的 ,若S的每个子半群都是S的一个缩回 .首先证明了群G为强可收缩半群的充要条件为G是一族初等Abel群的限制直积 ,接着得到完全单半群S强可收缩的充要条件是S G× (I×Λ) ,其中G为强可收缩群 ,I×Λ是矩形带 .还证明了一个半格是强可收缩半群的充要条件是它为局部有限树 .在这些结论的基础上最后得到一个半群是强可收缩半群的完整刻划 .     

强可收缩半群

称半群Ｓ强可收缩,若Ｓ的每个子半群都是它的一个缩回．本文逐次刻划了强可收缩的群、完全单半群、强可收缩的半格及正则半群的结构,在此基础上给出了任意强可收缩半群的结构定理．     

拓扑空间的收缩核与半收缩核(英)

本文的主要目的是建立收缩核与近似连续之间的联系，基于半连续函数概念，我们构造了一类收缩核，得到了关于这一概念的许多的性质与例子，证明并解释了半收缩核与拓扑折送之间的关系。