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非拓扑向量空间的拟拓扑向量空间
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作者 杨忠强 郑秋楠 《闽南师范大学学报(自然科学版)》 2024年第2期87-93,共7页
拟拓扑向量空间是在向量空间赋予一个拓扑使其满足数乘联合连续,加法分离变量连续的空间,给出生成非拓扑向量空间的拟拓扑向量空间的方法,由此可以得到仿紧的拟拓扑向量空间但不是拓扑向量空间.
关键词 拓扑向量空间 拟拓扑向量空间 仿紧
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拓扑保持映射下的拓扑性质
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作者 锜茜茜 林福财 《闽南师范大学学报(自然科学版)》 2024年第1期94-98,共5页
讨论在拓扑保持映射定义下的拓扑性质,得到了在T0分离公理的假设下拓扑保持映射是同胚映射.此外,还讨论拓扑保持映射下几类基数不变量,并得到拓扑保持映射保持连通性、紧性、仿紧性、可数紧性等.
关键词 拓扑保持映射 开映射 闭映射 稠密度 可分空间 仿紧空间.
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The Sequence-covering Compact Images of Paracompact Locally Compact Spaces 被引量:4
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作者 李进金 李克典 《Northeastern Mathematical Journal》 CSCD 2000年第4期463-468,共6页
This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally... This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces. 展开更多
关键词 sequence covering mapping compact covering mapping compact mapping quotient mapping paracompact locally compact space cs cover sn cover cs* cover
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Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications 被引量:1
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作者 Yi Li 《Applied Mathematics》 2013年第9期6-12,共7页
The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong c... The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497). 展开更多
关键词 MULTI-VALUED Mapping Totally Quasi- Ø -Asymptotically NONEXPANSIVE countable FAMILY of UNIFORMLY Totally Quasi- Ø -Asymptotically NONEXPANSIVE MULTI-VALUED Mappings Firmly Convergence
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Soft Locally Compact Spaces and Soft Paracompact Spaces 被引量:1
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作者 Sadi Bayramov Cigdem Gunduz 《Journal of Mathematics and System Science》 2013年第3期122-130,共9页
The concept of soft topological space was introduced by some authors. In the present paper, we investigate some basic notions of soft topological spaces by using new soft point concept. Later we give soft locally comp... The concept of soft topological space was introduced by some authors. In the present paper, we investigate some basic notions of soft topological spaces by using new soft point concept. Later we give soft locally compact space and the relationships between them are discussed in detail. Finally, we define soft paracompactness and explore some of its basic properties. 展开更多
关键词 Soft set soft point soft topology soft locally compactness soft paracompactness.
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Reflected BSDEs Driven by L&eacute;vy Processes and Countable Brownian Motions
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作者 Jean-Marc Owo 《Applied Mathematics》 2015年第14期2240-2247,共8页
A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the exis... A new class of reflected backward stochastic differential equations (RBSDEs) driven by Teugels martingales associated with Lévy process and Countable Brownian Motions are investigated. Via approximation, the existence and uniqueness of solution to this kind of RBSDEs are obtained. 展开更多
关键词 Backward DOUBLY Stochastic Differential Equations Lévy PROCESSES Teugels MARTINGALES countable BROWNIAN Motions
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Poincaré Inequalities on a Countable Set E and Ω={x:0≤x_i≤a, i=1,2,…,n}
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作者 陈文英 《Journal of Southwest Jiaotong University(English Edition)》 2005年第1期92-94,共3页
In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accord... In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accordingly the accurate expressions of Poincaré inequalities JB(=(f-μ(f))nJB)=_B≤cD(f, f) is presented to expand the research and application scope. As to inequalities for Ω={DK(x:0DK)≤x_i≤a, i=1,2,…,n}, the existing studies was usually made for n=2, but such an inequality was not the best. Therefore, the different values of n is discussed in this paper, and accordingly the accurate expressions of Poincaré inequalities is presented. 展开更多
关键词 countable set Poincaré inequalities Weight function
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On Spaces with a Locally Countable sn-network
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作者 KANG Bi-fang YAN Ming-gang LI Ke-dian 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第4期495-499,共5页
In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its applicatio... In this paper,spaces with a locally countable sn-network are discussed.It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network.As its application,almost-open and closed mappings(or finite-to-one and closed mapping) preserve locally countable sn-networks,and a perfect preimage theorem on spaces with a locally countable sn-network is established. 展开更多
关键词 locally countable family sn-network K-NETWORK cs-network
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Generalized Quasi-Variational Inequalities on Paracompact Sets
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作者 张昌斌 李岱 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第3期81-85, ,共5页
Taking advantage of result in [1], this paper studied generalized quasi variational inequalities on paracompact sets, unified and extended corresponding results in [4-6].
关键词 paracompact set generalized quasi variational inequality
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Star-countable Networks and Locally S-Countable Networks
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作者 燕鹏飞 《Northeastern Mathematical Journal》 CSCD 2004年第4期411-414,共4页
The concept of local s-countablity is introduced, and the relations between locally s-countable collections and star-countable collections are discussed.
关键词 locally s-countable star-countable cs-network cs-network
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生成式人工智能的算法风险及治理基点 被引量:24
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作者 陈兵 董思琰 《学习与实践》 CSSCI 北大核心 2023年第10期22-31,共10页
分类分级作为我国当前算法治理体系和对生成式人工智能服务监管的共同原则,是应对生成式人工智能算法风险的重要切入点。为应对算法分类分级治理具体标准不明、规范化与体系性不强、具体制度设计与分类分级原则衔接不严谨等问题,应进一... 分类分级作为我国当前算法治理体系和对生成式人工智能服务监管的共同原则,是应对生成式人工智能算法风险的重要切入点。为应对算法分类分级治理具体标准不明、规范化与体系性不强、具体制度设计与分类分级原则衔接不严谨等问题,应进一步推动分类分级与覆盖算法应用全生命周期的治理制度紧密衔接,探索构建以专门性、专业性法律规范为主,其他规范性文件为补充的,兼具稳定性和灵活性的算法治理法律规则体系,实现多元主体协同、制度设计优化、治理工具创新的同频共振,推动生成式人工智能监管落实。 展开更多
关键词 分类分级治理 算法备案 算法安全评估 算法问责 生成式人工智能
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A Note on Weakly-α-<i>I</i>-Functions and Weakly-α-<i>I</i>-Paracompact Spaces
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作者 Shi-Qin Liu 《Open Journal of Discrete Mathematics》 2012年第4期142-144,共3页
This paper introduces the new notion of weakly-α-I-functions and weakly-α-I-paracompact spaces in the ideal topo-logical space. And it obtains that some properties of them.
关键词 Weakly-α-I-Open Set Weakly-α-I-Functions Weakly-α-I-paracompact Spaces
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广义L-拓扑空间的可数仿紧性
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作者 张敏 王小霞 刘媛媛 《湖北大学学报(自然科学版)》 CAS 2023年第2期301-304,共4页
将L-拓扑空间中的可数仿紧性引入到广义L-拓扑空间中,研究广义L-拓扑空间中的广义可数仿紧性.基于α-远域族、α-局部有限等概念,利用类比和分析的方法,给出广义L-拓扑空间中广义可数仿紧集的概念,研究其基本性质.并证明了广义可数仿紧... 将L-拓扑空间中的可数仿紧性引入到广义L-拓扑空间中,研究广义L-拓扑空间中的广义可数仿紧性.基于α-远域族、α-局部有限等概念,利用类比和分析的方法,给出广义L-拓扑空间中广义可数仿紧集的概念,研究其基本性质.并证明了广义可数仿紧性具有闭遗传性、弱拓扑不变性等性质,该研究为广义L-拓扑空间的相关理论研究提供一定的参考. 展开更多
关键词 广义L-拓扑空间 可数α-远域族 α-局部有限 广义可数仿紧集
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仿紧正则locale的紧正则反射
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作者 任春蕾 孙向荣 《江苏师范大学学报(自然科学版)》 CAS 2023年第2期43-46,共4页
在locale范畴中讨论仿紧locale的性质,证明仿紧正则locale是正规的.通过正规locale的插入性,给出正则理想格CR(L)是仿紧正则locale的紧正则反射的构造性描述.
关键词 仿紧正则locale 紧正则反射 正规locale
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The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures
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作者 Philip C. Jackson 《Advances in Pure Mathematics》 2023年第4期198-205,共8页
This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers i... This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis. 展开更多
关键词 INFINITY countable DIAGONALIZATION Real Numbers Tree Structure Infinity Tree Continuum Hypothesis
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G-可数紧空间
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作者 刘丽 《扬州大学学报(自然科学版)》 CAS 北大核心 2023年第6期6-9,33,共5页
在一般空间中,在G-方法的基础上,从G-收敛和G-聚点出发,引入了G-可数紧空间,讨论其基本性质,并研究了G-可数紧性与G-序列紧性、可数紧性之间的关系.
关键词 G-方法 G-收敛 G-聚点 G-可数紧
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关于具有Pytkeev∗网空间的注记
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作者 邵辉 刘鑫 《宁德师范学院学报(自然科学版)》 2023年第3期225-228,234,共5页
讨论具有特定Pytkeev^(*)网的空间的度量性质,证明点可数的Pytkeev^(*)网是拟k网,并给出例子说明反之并不成立,从而得到具有点可数Pytkeev^(*)网的M空间是可度量的.最后给出了具有点可数Pytkeev^(*)网的可数紧空间是紧可度量的直接证明.
关键词 拓扑空间 Pytkeev^(*)网 度量空间 点可数
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相对拓扑的一些性质 被引量:11
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作者 严维军 王延庚 卫国 《纯粹数学与应用数学》 CSCD 2003年第3期223-226,共4页
讨论了相对超正则的充要条件及相对拓扑空间在映射下的一些性质,并定义了两类新的相对拓扑空间,给出了它们的一些性质.
关键词 Y在X中超正则 Y在X中可数紧 Y在X中Lindelof Y在X中可数1-仿紧 Y在X中弱仿紧 Y在X中几乎弱仿紧
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L-Fuzzy拓扑空间中一种新型的强F仿紧性 被引量:32
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作者 史福贵 郑崇友 《模糊系统与数学》 CSCD 1995年第3期40-48,共9页
本文引入一种新型的强F仿紧性─—Ⅲ型强F仿紧性,它是基于α-局部有限族概念提出的,这种α-局部有限族概念可用于刻划强F可数紧性。
关键词 强F可数紧性 LF拓扑空间 仿紧性 强F仿紧性
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遗传中紧空间与散射分解 被引量:4
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作者 燕鹏飞 涂振坤 《数学杂志》 CSCD 北大核心 2005年第1期107-110,共4页
本文证明了可数仿紧 (中紧、亚紧 )空间有类似 Junnila的刻画 ,遗传中紧空间不具有类似 Junnila的刻画 ,并给出了每个散射分解有紧有限的开膨胀的充要条件 .
关键词 中紧空间 遗传中紧 可数仿紧(中紧、亚紧) 紧有限 散射分解
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