Degree of Compactness in I-fuzzy Topological Spaces

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.

Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces

In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given. Some examples are illustrated.

The Hyperspace of the Regions below Continuous Maps with the Fell Topology

For a Tychonoff space X, we use ↓USCF（X） and↓CF（X） to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0, 1] with the subspace topologies of the hyperspace Cldf（X × I） consisting of all non-empty closed sets in X × I endowed with the Fell topology. In this paper, we shall show that there exists a homeomorphism h： ↓USCF（X） → Q = [-1, 1]^∞ such that h（↓ CF（X）） ： co ： {（Xn） E Q ｜ limn→ ∞ xn = O} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X.

Almost Fuzzy Compactness in L-fuzzy Topological Spaces

In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.

On the Behaviors of Hyperspace Topologies for Subspaces

For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.

Degrees of Fuzzy Compactness in I-Fuzzy Topological Spaces

In this paper, the concept of degree of fuzzy compactness in I-fuzzy topological spaces is introduced by means of inequation. Its properties are discussed.

The hyperspace of the regions below of all lattice-value continuous maps and its Hilbert cube compactification

Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.

紧凑型混合励磁三相饱和铁芯型故障限流器

加装饱和铁芯型故障限流器是限制高压系统短路电流的有效方法,但其需要与外加的限流空心电抗器配合,导致整个限流系统占地面积和体积很大。因此,基于非正交解耦原理提出了一种紧凑型混合励磁三相饱和铁芯型故障限流器(compact hybrid-biased three-phase saturated core fault current limiter,CTFCL),其具有占地面积和体积小的优点。首先,提出了含非正交解耦绕组的CTFCL拓扑。其次,建立了CTFCL的等效电磁路模型,分析了其工作原理。然后,给出CTFCL的参数设计准则,搭建了220 kV的有限元模型,仿真验证了CTFCL的限流效果和电磁特性。最后,设计并研制出小容量样机,开展了实验研究。仿真和实验结果均证明了该文所提CTFCL的有效性,CTFCL对各种短路均有良好的限制效果,且对比得到CTFCL限流系统占地面积和体积较传统三相SCFCL限流系统分别减少了44%和26%,适合实际高压系统的安装与应用。

NL-fuzzy拓扑空间中的N-紧性

利用α-远域族定义了NL-fuzzy拓扑空间中的N-紧性,借助α-分子网,模糊滤子以及模糊滤子基的概念给出其等价刻画。证明了N-紧性具有拓扑不变性以及有限多个N-紧集的并仍为N-紧集等性质。

拓扑空间中的理想收敛

用理想收敛结构解决定向拓扑的刻画问题,给出理想S极限和理想广义S极限可拓扑化的充要条件.结果表明:T0拓扑空间上的定向拓扑、理想S极限拓扑和理想广义S极限拓扑相同;定向空间中的理想S收敛是拓扑的当且仅当其为c-空间;定向空间中理想广义S收敛是拓扑的当且仅当其为局部强紧空间.

指数有界n阶α次积分C群的紧性

利用指数有界n阶α次积分C群及其次生成元的定义,并借助经典算子理论的研究方法,给出了指数有界n阶α次积分C群紧的定义,从而推导出指数有界n阶α次积分C群的紧性的一些性质。

TOPOLOGICAL STRUCTURE OF A FUZZY FUNCTION SPACE——THE POINTWISE CONVERGENT TOPOLOGY AND COMPACT OPEN TOPOLOGY

In the area of fuzzy topology, researches have been carried out in China and abroad in recent years. But the theory of the fuzzy function space, which is apparently important in fuzzy topology, has not been established yet. The important theories of compactness, separation and uniformities on a fuzzy topological space, related closely to the discussion of topological structure of the fuzzy function space, are so complicated that the research on the subject is rather difficult.

Topology change and emergent scale symmetry in compact star matter via gravitational wave detection

Topological structure has been extensively studied and confirmed in highly correlated condensed matter physics. We explore the gravitational waves emitted from binary neutron star mergers using the pseudoconformal model for dense nuclear matter for compact stars. This model considers the topology change and the possible emergent scale symmetry and satisfies all the constraints from astrophysics. We find that the location of the topology change affects gravitational waves dramatically owing to its effect on the equation of state. In addition, the effect of this location on the waveforms of the gravitational waves is within the ability of the on-going and up-coming facilities for detecting gravitational waves, thus suggesting a possible way to measure the topology structure in nuclear physics.

Fixed Point Theorems for Increasing Operators of None－continuity and None－compactness Conditions

In this paper, the fixed point theorems of composite set-valued increasing operators are given. As a corollary, the fixed point theorem for increasing operator of none-continuity and nonecompactness conditions is also given. Some relevant results are improved and generalized.

饱和集拓扑空间的一些性质

利用拓扑学的研究方法,首先给出了饱和集的交、并以及拓扑等概念。在此基础上,得到一些饱和集的拓扑性质。具体包括:饱和集拓扑空间(Xf,τ)的紧子空间在交、并运算下保持不变;利用闭映射的性质证明了若(Xf,τ)满足T2,正则以及第二可数性公理,则其在完备映射下的像也保持这种性质。

半群作用的拓扑熵及其性质

在半群作用下利用分离集和生成集构造上容量拓扑熵、Bowen拓扑熵、packing熵.讨论了三者之间在半群作用下的性质和关系.

Soft Locally Compact Spaces and Soft Paracompact Spaces

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.

针对无标度网络的紧凑路由方法

衡量一种路由算法优劣的两个重要指标是路由表的大小和路径的长度,但这两个方面通常是互相矛盾的.紧凑路由(compact routing)研究旨在设计路由算法在这两个指标上获得优化的平衡(tradeoff).目前,已有许多学者针对任意拓扑的网络提出了普适(universal)的紧凑路由方法(compact routing scheme).但是,真实的网络都具有特定的拓扑,普适的紧凑路由方法并没有利用真实网络呈现的特定拓扑特征,因而在这类网络上未必能取得最优的性能.最近的研究发现,许多真实网络都具有无标度特征和强聚集特征,利用这两类拓扑特征,提出了一种针对这类网络的紧凑路由方法.该路由方法将网络看成是由一个骨干树和一些捷径组成,在任意源节点和目的节点之间路由,使用路径的长度不超过它们的最短路径长度加上一个整数b.路由表大小限制在O(clog2n)比特,其中,b和c是由网络结构决定的参数.实验结果表明,在无标度网络上,b和c可以同时取较小的值.与以往的紧凑路由方法相比,该方法在平均性能上表现更好.

紧性的非标准定义及其性质

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.一方面,这种新的定义与一般的紧性定义是一致的;另一方面,这种新的定义方法简化了原有的概念和结论,使它们的本质特性更为清晰,因而在一定程度上发展了拓扑空间中原有的紧性理论.

一类代换系统及其超空间系统

考察了非本原代换及其诱导的集值映射的动力学性质.给出了该类代换诱导的超空间系统是Li-Yorke混沌的一个充分条件.证明了这类代换的拓扑熵为0,并且给出了这类代换诱导的集值映射具有零拓扑熵的一个充分条件.