拓扑完备空间

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

We introduce the uniform Hausdorff metric H on the space 〓 offuzzy complex numbers and investigate the topological structure of 〓.We show the completeness of 〓 and study on 〓 limits of thesequence of fuzzy complex numbers,metrical and leverwise convergence,and relation between metrical convergence and leverwise convergence.Weprove the equivalence theorem of metrical convergence and leverwiseconvergence on 〓.

在模糊复数空间〓上引进一致Hausdorff度量H，讨论了模糊复数空间的拓扑结构，证明了的完备性，并在完备的模糊复数度量空间上研究了模糊复数列的极限、度量收敛和水平收敛，讨论了度量收敛与水平收敛之间的关系，在上证明了度量收敛与水平收敛的等价性定理。

In thisthesis, we first extend the vanishing theorem due to Lawson, Simons and Xinto the case of compact submanifolds of a hyperbolic space. Thus, by using thenew vanishing theorem for homology groups, we prove the topological spheretheorem for complete submanifolds in a hyperbolic space. Hence we generalizethe Shiohama-Xu topological sphere theorem.

本文进一步将Lawson-Simons-Xin同调群消没定理拓广到双曲空间中紧致子流形的情形，并运用这一新的同调群消没定理证明了双曲空间中完备子流形的拓扑球面定理，从而推广了Shiohama-Xu的拓扑球面定理。

A multi-level hierarchical image representation that preserves topological relation equivalency and a set of well-complete functional architecture that efficiently reflects this representation are presented, and the digital Jordan curve theorem is validated.

基于复形理论定义了数字图像空间的拓扑元素及其性质，在此基础上提出一套完备的保持拓扑等价性的层次表达数字图像的数学模型体系框架，并验证了层次表达结构中的Jordan曲线定理。

Firstly,we prove that the open mapping theorem to situations where spaces are normed and the graphs of convex maps are complete.

其次，我们还推广了在可度量化拓扑线性空间中，完备图的线性映射是开映射的结果。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

The measurement in set theory, the properties of Metric Space, Measurement Topology, Measurable Space, Perfect Metric Space and its application in first order circuit are explored in this paper.

本文论述了集合上的度量、度量空间的性质、度量拓扑、可度量化空间、完备度量空间、及一阶电路中的度量空间。

The relation between the completeness of several local convex topology in normed vector space and that of induction topology of its unit ball was pointed out in this paper.

本文指出了赋范线性空间上的一些局部凸拓扑的完备性与它的单位球上相应的诱导拓扑的完备性之间的关系。

Prove the same completeness of the two topological vector space of linear topological equivalence.

证明两个线性拓扑等价的拓扑向量空间具有相同的完备性。

Then,it notices that all infi-nite matrix operators between the sequence spaces with the WGHP may form a topologicalalgebra.It also studies the weak sequentially completeness of this class of topological al-gebras and some other basic properties.

其次发现了具有WGHP序列空间上无穷矩阵算子所成之拓扑代数，并研究了这类无穷矩阵拓扑代数的弱序列完备性等一些基本性质。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。