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In the first part, the concepts of the completely normal spaces and strong completely normal spaces in L-topological spaces are defined, which are the generalization of the completely normal spaces in general topological spaces. They are some good properties such as hereditary, weakly homeomorphism invariant properties, good L-extension, but they arent producible in general.

第一部分的主要内容如下：第一部分这一部分是将一般拓扑学的完全正规分离性的概念推广到了L-拓扑空间，给出了L-拓扑空间的完全正规分离性和强完全正规分离性的定义并讨论了它们的若干性质，比如，它们都是可遗传的，弱同胚不变的，"Lowen意义下好的推广"等。

-homology inverse and group homology inverse are defined in this paper on categories of topologicalspace with base point.

在点标拓扑空间范畴中引进了-同调逆和群同调逆的概念，并讨论了它们存在的条件和性质。

Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.

本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。

The mathemationcal formulation is based on a locally convex topological space for arbitrage freeness,approximate arbitrage freeness and no free lunc hes.

本文研究具有摩擦的证券市场中资产定价，即在局部凸拓扑空间中弱与强无套利、弱与强近似无套利及弱与强没有免费午餐。

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 existence of the minimal and maximal fixed points for order preserving set-valued operators on semi-ordered sets and semi-ordered topological spaces was analyzed.

讨论了半序集和半序拓扑空间中保序集值算子的最小与最大不动点的存在性。

Some important properties of L-topological spaces, induced topological spaces, fuzzy real lines and fuzzy metric spaces in topology on lattices are obtained.

在格上拓扑中，对L-拓扑空间、诱导拓扑空间、fuzzy 实直线和fuzzy度量空间等的性质研究，得到了一系列重要的结果。

Finally,as an application of the theorem,a new minimax inequality is given in general topological spaces.

最后，应用此非空交定理，在没有凸结构的一般拓扑空间中得到了一个新的极大极小不等式。

Based on the nonstandard topology definition and enlarged model, the concept of compactness in the topological space are described and characterized in this paper.

在非标准扩大模型和拓扑的非标准定义基础之上，对拓扑空间中紧性的概念及相关结论进行了描述和刻画。

In chapter 2, by virtue of the properties of partially ordered F-type topological space, we establish some fixed point theorems of increasing mappings in this kind of space. At the same time, we investigate the existence of maximum fixed point and minimum fixed point of increasing mappings on an order interval.

第二章，利用半序F-型拓扑空间的基本性质，建立这类空间上单调增映射的不动点定理，研究其序区间上单调增映射的最大、最小不动点的存在性。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。