L─Fuzzy拓扑空间的局部连通性

文［１］曾在广义拓扑分子格中提出了一种连通性。本文在Ｌ—ｆｕｚｚｙ拓扑空间中给出了这种连通性的几种刻划，并引入了Ｌ—ｆｙｚｚｙ拓扑空间的局部连通性。这种局部连通性是有限可乘的，商序同态保持的且是好的推广。另外，ｆｕｚｚｙ实直线是局部连通的。     

关于子基的局部连通性

在粗燥集理论研究中,覆盖方法的应用越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.在最近由它们导入的关于子基的连通性基础上,给出了关于子基的局部连通性概念,并研究它的性质,得到一般拓扑学中局部连通性的一种推广.     

Connectedness in Metric Frames

A new metric diameter for a locally connected metric frame is constructed which is finer than the original one. Amongst other results, this construction allows a proof that the category of uniformly locally connected metric frames and uniform frame maps is reflective in the category of locally connected metric frames and uniform frame maps. Mathematics Subject Classification (2000) 54A05.     

弱紧局部一致凸空间中的度量投影

本文研究了弱紧局部一致凸空间中度量投影的弱连续性,将Ｂ．Ｂ．Ｐａｎｄａ和Ｏ．Ｐ．Ｋａｐｏｏｒ的相应结论推广到更一般的弱紧局部一致凸空间．最后给出了局部一致凸点的一个必要条件．     

Local Accuracy for Radial Basis Function Interpolation on Finite Uniform Grids

We consider interpolation on a finite uniform grid by means of one of the radial basis functions (RBF) φ(r)=r^γ for γ>0, γ2 or φ(r)=r^γ ln r for γ2 ₊. For each positive integer N, let h=N⁻¹ and let {x_i: i =1, 2, …, (N+1)^d} be the set of vertices of the uniform grid of mesh-size h on the unit d-dimensional cube [0, 1]^d. Given f: [0, 1]^d→ , let s_h be its unique RBF interpolant at the grid vertices: s_h(x_i)=f(x_i), i=1, 2, …, (N+1)^d. For h→0, we show that the uniform norm of the error f−s_h on a compact subset K of the interior of [0, 1]^d enjoys the same rate of convergence to zero as the error of RBF interpolation on the infinite uniform grid h ^d, provided that f is a data function whose partial derivatives in the interior of [0, 1]^d up to a certain order can be extended to Lipschitz functions on [0, 1]^d.     

灰拓扑空间的连通性

研究灰拓扑空间的连通性,给出了灰拓扑空间连通定义和有关定理,并且研究了灰连通分支。     

带约束条件集值优化问题近似Henig有效解集的连通性

研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.     

Quantah的连通性

The concepts of connectedness and locally connectedness is introduced for right-side idempotent quantales. Some properties of connected quantale are studied, and then the equivalent characterization of connected quantale is also given.     

Connectedness of curve complex of surface

For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C(Sg) can be connected by an edge path,and C(Sg) has an infinite diameter. We show that for 0 ≤i≤3g-5,two i-simplices can be connected by an(i +1)-path in C(Sg),and the diameter of C(Sg) under such a distance is infinite.     

Interior Operators and Topological Connectedness

Abstract

A categorical notion of interior operator is used in topology to define connectedness and disconnectedness with respect to an interior operator. A commutative diagram of Galois connections is used to show a relationship between these notions and Arhangelskii and Wiegandt's notions of connectedness and disconnectedness with respect to a subclass of topological spaces. Examples are included.     

A Link Between Two Connectedness Notions

The composition of two previously introduced Galois connections is used to provide a wider perspective on the Clementino–Tholen connectedness versus separation Galois connection. Moreover, a link between this and Castellini's connectedness–disconnectednes Galois connection is also presented.     

Connectedness with Respect to a Closure Operator

A notion of connectedness with respect to a closure operator C and a class of monomorphisms N is introduced in an arbitrary category X. It is shown that under appropriate hypotheses, most classical results about topological connectedness can be generalized to this setting. Examples that illustrate this new concept are provided.     

On the Connectedness of Probabilistic Constraint Sets

We prove a result on the connectedness of (abstract) probabilistic constraints P(h(x,)0)p without any assumption on the distribution of . An application to storage level constraints is discussed briefly. Illustrating examples are provided and a simple criterion for the required condition is given in the case of linear h.     

粗糙有限状态机的可恢复性与连通性

利用代数的方法研究了粗糙有限状态机的可恢复性与连通性,通过前驱与后继的关系,给出了粗糙有限状态机的可恢复性、连通性与可分离性的一些刻画,讨论了粗糙有限状态机的一些基本性质.     

Connectedness of the efficient set in strictly quasiconcave vector maximization

In this paper, the concepts of quasiconcave set and strictly quasiconcave set are introduced. By using these concepts, we get a new sufficient condition for the efficient outcome set to be connected. This leads to the connectedness of the efficient solution set in strictly quasiconcave vector maximization under the mild condition that the efficient frontier is closed.The authors would like to thank Professor E. U. Choo and the referees for their many valuable comments and helpful suggestions.     

关于子基的强连通性

在LF拓扑空间中借助于相对闭包引入了关于子基的强连通性的概念,研究了它的一些基本性质和等价刻画.结果表明,这种强连通性保持了LF拓扑空间中已有连通性的许多类似性质     

超空间2^X的连通性及其相关性质

研究了赋予Vietoris拓扑的超空间2X的连通性及其相关性质.这改进了Micheal[1]的一个定理的结论.     

Contractibility and Connectedness of Efficient Point Sets

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

A Note on the Connectedness of the Invertible Group of a Nest Algebra

The connectedness of the invertibles question for arbitrary nest has been reduced to the case of the lower triangular operators with respect to a fixed orthonormal basis en for n 1. For each f ∈ H∞, let Tf be the Toeplitz operator. In this paper we prove that Tf can be connected to the identity through a path in the invertible group of the lower triangular operators if f satisfies certain conditions.