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 共查询到19条相似文献,搜索用时 62 毫秒
1.
研究L-值随机变量(其中L是闭集格或分子生成格与格上拓扑学有关)。受到已有文献中研究L-拓扑空间的思想、方法和技巧的启发,定义FLc(Rn)={A∈LRn对每个余素元,α{x∈Rn A(x)≥α}是Rn中的非空紧集}上一个分明拓扑TFLc以及L-子集族上的三种度量。在此基础上定义几种L-值随机变量并讨论了它们的初步性质。  相似文献   

2.
完全分配格的谱论与拓扑分子格   总被引:1,自引:1,他引:0  
樊太和 《数学学报》1992,35(5):598-605
本文借助于完全分配格的谱理论是首先证明分子格范畴同构于某连续偏序集范畴子范畴,然后利用上述同构,证明分子格上余拓扑同构于其中分子之集上。与分子序密切相关的某分明拓扑,从而就给“重域”“远域”这两个基本概念以合理解释,并证明许多拓扑分子格性质的研究可以化为相应的拓扑空间性质的研究.“重域”概念的引入,使 fuzzy 拓扑学的研究发生了根本变化,导致了有点派的兴起。而“远域”的引入,则导致因更广的拓扑分子格理论的产生,从而把 Fuzzy 拓扑为学纳入了拓扑格的范畴.本文中我们首先建立分子格范畴与连续偏序集范畴某子范畴的同构,从而把二者的研究紧密结合起来,然后借助上述同构把拓扑分子格中的问题的研究化为连续偏序集中问题去考虑,通过这种转化,我们将会看到,“重域”,“远域”等基本概念确为 fuzzy 拓扑学,拓扑分子格中唯一合理的点与集合的邻属关系,而择一原理这条fuzzy 拓扑学中的基本原理成立的原因也就变得很清楚。本文中凡未定义的概念请参看[4].  相似文献   

3.
拓扑均衡支撑分子格   总被引:1,自引:0,他引:1  
何伯镛 《数学学报》1992,35(5):642-651
本文从讨论完备 Heyting 代数与完备原子 Boole 代数的内在联系出发,给出一类抽象格的若干结构定理,然后建立拓扑均衡支撑分子格的框架,使有点拓扑格理论与不分明拓扑学获得进一步统一.  相似文献   

4.
陈鹏  史福贵 《数学进展》2007,36(5):586-592
本文对Erceg-伪度量做了进一步简化,指出了史福贵的点式伪度量和Erceg-伪度量间的关系,并给出了Erceg-伪度量的一些性质.  相似文献   

5.
由子基生成的内部算子和闭包算子   总被引:16,自引:1,他引:15  
李进金 《数学进展》2006,35(4):476-484
本文研究粗糙集与拓扑空间的关系,统一地使用拓扑空间中的集合关于子基的内部和闭包来研究粗糙集理论和覆盖广义粗糙集理论中的下近似集和上近似集,以及由它们导出的关于子基的开集,导集,闭集,边界.研究这两个概念及由它们导出的相关概念的性质不仅对于粗糙集理论,而且对于拓扑学本身都有重要的理论和实际应用意义.  相似文献   

6.
林寿 《数学进展》2002,31(6):503-509
广义度量空间理论是一般拓扑学研究的重要课题。本文综述了90年代广义度量空间理论的成就,分析了它的主要研究课题,所取得的重要结果是国内学者在该方向的贡献。  相似文献   

7.
本文在可数多个分子格的乘积上构造了一个乘积点式p·q·度量函数,从而证明了点式p·q·度量分子格的可数积是可点式p·q·度量化的.  相似文献   

8.
郑崇友、樊磊、崔宏斌著的((Fra与连续格》一书(以下简称《格》)已由首都师范大学出版社出版.《格》是我国第一部系统论述Frame理论和连续格理论的学术专著,是适合于格与拓扑方向研究生和高年级本科生使用的好教材.1《格》提供了广义空间理论的一个要览按Bourbaki...  相似文献   

9.
格上点式拓扑的基数函数   总被引:2,自引:1,他引:1  
目前,不分明拓扑学的研究正迅速地向拓扑格的理论迈进。文[1]总结了过去的工作,较为全面地在一种合理而广泛的框架下建立了格上点式拓扑的远域系结构,以及Moore-Smith收敛的理论,为格上拓扑学的进一步研究奠定了基础。本文就是在这种较为广泛而又合理的拓扑格的背景下,以“远域”为工具,建立了格上拓扑学的各种基数函数的概念,讨论它们之间的关系,并推广了若干在一般拓扑学中较为著名的基数不等式。 在本文的讨论中,我们不涉及任何“开”的概念,仅以“闭”的概念作为基本的出发点,而获得了格上基数函数的许多性质。这又一次证明,在格上拓扑理论的研究中,“闭”的概念更为基本,更反映拓扑学的本质。有了这些讨论,人们对格上代数理论的认识,将会有深一层的了解。  相似文献   

10.
分子格的极大点的相通支及其应用   总被引:2,自引:0,他引:2  
在一般的分子格中建立类似于F集中的“点的支撑”的概念-极大点的相通支,得到分子格的最大元的一种分解,并定义了TML中元的良聚点、良导元,讨论了它们的性质。结果表明它们具有F拓扑学中的导集的许多好的性质。  相似文献   

11.
对L-拓扑中已有度量理论的研究进展作一个简要的介绍和评述,力图使读者了解L-拓扑中度量理论的发展概况和发展方向。  相似文献   

12.
Quantitative measurement of the similarity of partitions is a problem of particular relevance to the social and behavioral sciences, where experimental procedures necessitate the analysis and comparison of partitions of objects. Since metrics used for this purpose vary considerably in computational complexity. I describe two related metric models that permit methodical enumeration of metrics which may be useful and computationally tractable. Twelve metrics on partitions are identified in this way. Five of them have appeared in the literature, while seven appear to be new. Four of them seem difficult to compute, but efficient algorithms for the remaining eight exist and exhibit time complexities ranging from O(n) to O(n3), where n is the number of objects in the partitions. These algorithms are all based on lattice- and graph-theoretic representations of the computational problems.  相似文献   

13.
14.
Given two points a=(a1,…,an) and b=(b1,…,bn) from Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), we study properties of the total variation of f on introduced by the first author in [V.V. Chistyakov, A selection principle for mappings of bounded variation of several variables, in: Real Analysis Exchange 27th Summer Symposium, Opava, Czech Republic, 2003, pp. 217-222] such as the additivity, generalized triangle inequality and sequential lower semicontinuity. This extends the classical properties of C. Jordan's total variation (n=1) and the corresponding properties of the total variation in the sense of Hildebrandt [T.H. Hildebrandt, Introduction to the Theory of Integration, Academic Press, 1963] (n=2) and Leonov [A.S. Leonov, On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle, Math. Notes 63 (1998) 61-71] (nN) for real-valued functions of n variables.  相似文献   

15.
Given a=(a1,…,an), b=(b1,…,bn)∈Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), denote by the Hildebrandt-Leonov total variation of f on , which has been recently studied in [V.V. Chistyakov, Yu.V. Tretyachenko, Maps of several variables of finite total variation. I, J. Math. Anal. Appl. (2010), submitted for publication]. The following Helly-type pointwise selection principle is proved: If a sequence{fj}jNof maps frominto M is such that the closure in M of the set{fj(x)}jNis compact for eachandis finite, then there exists a subsequence of{fj}jN, which converges pointwise onto a map f such that. A variant of this result is established concerning the weak pointwise convergence when values of maps lie in a reflexive Banach space (M,‖⋅‖) with separable dual M.  相似文献   

16.
TheCartesianClosednessoftheCategoryCDLandFunctionSpacesonTopologicalCDL'sYangZhongqiang(杨忠强)(DepartmentofMathematics,ShaanxiN...  相似文献   

17.
在完全分配格上定义L—smooth点式拟一致结构概念,并研究它与点式拟一致结构之间的关系以及与smooth拓扑之间的关系,给出分解定理、表现定理及构造条件。  相似文献   

18.
Let X be a metric space with metric d, c(X) denote the family of all nonempty compact subsets of X and, given F,G∈c(X), let e(F,G)=supxFinfyGd(x,y) be the Hausdorff excess of F over G. The excess variation of a multifunction , which generalizes the ordinary variation V of single-valued functions, is defined by where the supremum is taken over all partitions of the interval [a,b]. The main result of the paper is the following selection theorem: If,V+(F,[a,b])<∞,t0∈[a,b]andx0F(t0), then there exists a single-valued functionof bounded variation such thatf(t)∈F(t)for allt∈[a,b],f(t0)=x0,V(f,[a,t0))?V+(F,[a,t0))andV(f,[t0,b])?V+(F,[t0,b]). We exhibit examples showing that the conclusions in this theorem are sharp, and that it produces new selections of bounded variation as compared with [V.V. Chistyakov, Selections of bounded variation, J. Appl. Anal. 10 (1) (2004) 1-82]. In contrast to this, a multifunction F satisfying e(F(s),F(t))?C(ts) for some constant C?0 and all s,t∈[a,b] with s?t (Lipschitz continuity with respect to e(⋅,⋅)) admits a Lipschitz selection with a Lipschitz constant not exceeding C if t0=a and may have only discontinuous selections of bounded variation if a<t0?b. The same situation holds for continuous selections of when it is excess continuous in the sense that e(F(s),F(t))→0 as st−0 for all t∈(a,b] and e(F(t),F(s))→0 as st+0 for all t∈[a,b) simultaneously.  相似文献   

19.
王晓佳 《应用数学》2012,25(1):224-230
本文讨论了线性时滞微分方程的点态退化问题.借助于矩阵的有关知识,我们给出了判定n阶时滞微分方程点态退化的充分必要条件及代数判据.  相似文献   

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