扑空

First of all, the dissertation proves that the three structures are pairwisely isomorphic—the Boolean Algebra formed by the value range topological space, the Boolean Algebra by knowledge nodes, and the Boolean Algebra by data sub-classes. Thus the essential relations between the three Boolean Algebras are constructed. Furthermore, The three structures have the same multiplying mechanism.

首先，论文从理论上证明了由数值域拓扑空间形成的布尔代数、由知识结点集形成的布尔代数、和由数据子类结构集形成的布尔代数在结构上有两两同构的关系，从而建立了了这三者在本质上的联系，并且论证了它们具有相同的"繁衍"机制。

As the layer structure of lattice, relative separation properties and relative compactness in L-fuzzy topological spaces are more complex than that in general topological spaces.

由于层次结构的存在，L-fuzzy拓扑空间中的相对分离性和相对紧性较一般拓扑学中的相对分离性与相对紧性复杂得多。

After analyzing the merit and lack of 9I model, the main idea is proposed: to distill some basic topological relations from 9I model, of which the composite topological relations of complex objects are made up. In detail, the composite topological relationships between region and region, line and line, line and region are particularly discussed;(2)Analyze the characteristics and inner relations of cadastral features. According to the expressional model of complex topological relations, the author discovers the possible topological relations between parcels, parcel lines and parcel points. In addition, sum up the general topological relationship rules of cadastral data.(3) Then the topological relations model is extended to the spatio-temporal data. Time in cadastral database and change semantic are discussed. It's redefined that spatio-temporal topological relations is composed of time, location, status and event relation. Spatio-temporal topological relationships can be represented by extended 4I model. Taking cadastral parcels as example, there are different possible spatio-temporal topological relationships between parcels when they are extended, shrunken, split, merged or others. Thus, some deductions are drawn that, for example, if parcels have be coexisting for some time they are impossible to be overlapped. Furthermore, the parents of parcels alternated and their possible change types can be detected by their spatio-temporal topological relationships.(4) Before carrying out the experiment, the calculation method must be designed.

具体研究工作及成果如下：（1）根据点集拓扑理论中与拓扑空间相关的概念，本文对空间的点、线、面进行了重新定义，以区分对象的复杂性；分析了9I模型在表示简单对象方面的优点，以及在表达复杂对象上的不足，阐述了本文的研究思路和解决方案，并以复杂的面面、线线和线面为例详细探讨了复合拓扑关系的表达方法；（2）分析了地籍权属数据和地类数据的内涵、特点和要素之间的联系，根据复杂对象的拓扑关系表达模型，本文讨论了宗地、界址线、界址点之间，图斑、线状地物、零星地类之间可能存在的拓扑关系和形式化表达方法，归纳总结了地籍对象的拓扑关系满足的约束性规则；（3）将拓扑关系的研究延伸到时空领域，从地籍对象的时态性出发，本文阐述了地籍数据中时间的含义和变化语义描述的需要；从时间、位置、状态、事件等之间的拓扑关系方面，重新系统性地进行了时空拓扑关系的定义；研究了一维时间和二维空间的集成表达方式，以宗地、界址线为例，分析了变更前后不同时间区间里可能的拓扑关系，探讨了时空拓扑关系对时空变化操作类型和变化语义的推理方法和意义；（4）为实现空间拓扑关系的查询分析等应用，本文研究了空间拓扑关系的计算方法。

First,a proposition is presented:for a general kind of biobjective deci-sionmaking problemin real linear topological space satisfyiny someuniversal convexity assumpltions,the Pareto frontier is a piece-wise smoothconvex curve,each piece being either a Ⅰ-curve or a Ⅱ-curve.

对于满足一般凸性假设的实线性拓扑空间上的双目标决策问题，本文提出了"其非劣前沿为分段光滑的凸曲线，每一段要么是工型弧线，要么是直型弧线"的观点，据此详细研究了决策人的偏好与加权和问题之间的关系，提出了4种对话式决策方法，这些方法既适用于一类静态双目标决策问题，又可适用于一类双目标控制问题。

There is a simple way of associating a topological space with a graph .

有一种把一个拓扑空间同一个图联系起来的简单的方式。

Based on several examples, this paper introduces several kinds of particular topological space construction, which brought a series of conclusion.

摘要通过若干例题介绍了几种典型的拓扑空间构造法，并带来一系列的结论。

Seven definitions of the topological space were proposed and their sameness were proved.

本文给出了拓扑空间的七个定义，并通过循环证明的方法证明了它们的等价

Connectivity is one of the basic properties of topological space. R-strong connectivity is stronger than connectivity, and it has some good qualities.

连通性是拓扑空间的基本性质，R-强连通性比连通性要强，它具有一些良好的性质。

In this paper the equivalent of the various topologies on the closed setlattice of a topological space is investigated a sufficient and necessary condition for their equivalent is given.

本文对拓扑空间闭集格上的各种拓扑的等价性进行了研究，得到了它们等价的一个充分必要条件

We prove the strong compactness and N-compactness of fuzzy sets areequivalent in 〓 fuzzy topological space.

再次，证明了模糊集合的强紧性和良紧性在〓模糊拓扑空间中是等价的。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐