L-拟序集上的广义Alexandroff拓扑

在一类特殊的 L -拟序集上定义广义 Alexandroff拓扑 ,限制到通常的拟序集上就是 Alexandroff拓扑 ,并且该拓扑可以由其上的一族 Alexandroff拓扑取并得到。还证明任意一个拓扑空间的拓扑都可以表示为某个 L-拟序集上的广义 Alexandroff拓扑。     

L-拓扑空间的强拟半开集

在L-拓扑空间给出了强拟半开集和强拟半闭集的概念,并且讨论了它们的一些性质.     

L-拓扑空间中的拟紧度

借助于格己的蕴涵算子,在L-拓扑空间中引入了模糊集的拟紧度的概念.一个L-模糊集G是拟紧的当且仅当它的拟紧度pcom(G)=(T).我们还研究了拟紧度的一系列性质.     

L-拓扑空间中的半拟紧性

在L-拓扑空间中借助于半拟开L-集合和它们的不等式给出了半拟紧性的一个新定义,这里L是完备的DeMorgan代数。它也能够借助于半拟闭L-集和它们的不等式刻画。当L是完全分配的DeMorgan代数时,它的许多刻画被给出了。     

广义超度量矩阵的封闭性质

本文研究了广义超度量矩阵的封闭性质.证明了若A为非奇异的广义超度量矩阵,则A与A的转置的Hadamard积仍然是一个广义超度量矩阵,并且它的逆矩阵是一个对角占优的M矩阵.给出了两个广义超度量矩阵Hadamard积封闭的一个充分条件.最后,讨论了广义超度量矩阵的Perron补与和的封闭条件.     

r-拟半开L-集和r-拟半闭L-集

在L-fuzzy拓扑空间中引入r-拟半开L-集和r-拟半闭L-集,正则r-拟半开L-集和正则r-拟半闭L-集,同时讨论它们一些性质.     

拟序下非连续增算子新的广义不动点定理

运用序方法研究了拟序空间X中具A=CB型非连续增算子的广义不动点的存在性问题,证明了在拟序空间X中具A=CB型非连续增算子存在最小广义不动点和最大广义不动点.所得结果推广了相关结论.     

L-余拓扑Vs.广义粗集

引入L-余覆盖广义粗集的概念,证明研究该广义粗集的上、下近似与研究L-余拓扑的余子基生成的闭包和内部是等价的,并且以此为基础,讨论该广义粗集的性质.     

L-层次拓扑空间

在L-拓扑空间中,利用Dα-闭集推广了远域的概念,定义了L-子集的层次收敛,建立了网的层次收敛理论.     

拓扑序空间中的广义向量值均衡问题

利用一个KKM型定理,在拓扑序空间中,建立了关于广义向量值均衡问题解的某些新的存在性定理.     

Complete Congruences on Topologies and Down-set Lattices

From the work of Simmons about nuclei in frames it follows that a topological space X is scattered if and only if each congruence Θ on the frame of open sets is induced by a unique subspace A so that , and that the same holds without the uniqueness requirement iff X is weakly scattered (corrupt). We prove a seemingly similar but substantially different result about quasidiscrete topologies (in which arbitrary intersections of open sets are open): each complete congruence on such a topology is induced by a subspace if and only if the corresponding poset is (order) scattered, i.e. contains no dense chain. More questions concerning relations between frame, complete, spatial, induced and open congruences are discussed as well. Dedicated to Bernhard Banaschewski.     

Generalized Alexandroff Duplicates and CD 0(K) spaces

We define and investigateCD _Σ,Γ(K, E)-type spaces, which generalizeCD ₀-type Banach lattices introduced in [1]. We state that the space CD _Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].     

覆盖广义粗糙集的模糊性

在研究覆盖广义粗糙集的基础上,利用两个距离函数Hamming和Euclidean距离函数,结合模糊集的最近寻常集,引入了覆盖广义粗糙集模糊度的概念,给出了一种模糊度计算方法,并证明了该模糊度的一些重要性质。这些结果在覆盖广义粗糙集的理论研究和应用都发挥着一定作用。     

L-不分明化一致空间和L-不分明化一致拓扑

通过应用完全剩余格值逻辑语义的方法把不分明化一致空间和不分明化一致拓扑推广为L-不分明化一致空间和L-不分明化一致拓扑。并且讨论了L-不分明化一致空间和L-不分明化一致拓扑的一些基本性质。     

Wijsman and Hit-and-Miss Topologies of Quasi-Metric Spaces

The relationship between the Wijsman topology and (proximal) hit-and-miss topologies is studied in the realm of quasi-metric spaces. We establish the equivalence between these hypertopologies in terms of Urysohn families of sets. Our results generalize well-known theorems and provide easier proofs. In particular, we prove that for a quasi-pseudo-metrizable space (X,T) the Vietoris topology on the set P ₀(X) of all nonempty subsets of X is the supremum of all Wijsman topologies associated with quasi-pseudo-metrics compatible with T. We also show that for a quasi-pseudo-metric space (X,d) the Hausdorff extended quasi-pseudo-metric is compatible with the Wijsman topology on P ₀(X) if and only if d ^–1 is hereditarily precompact.     

Maps on Ultrametric Spaces,Hensel's Lemma,and Differential Equations Over Valued Fields

We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multidimensional Hensel's Lemma follow from our result. We give an easy proof that the latter holds in every henselian field. We also prove a basic infinite-dimensional Implicit Function Theorem. Further, we apply the criterion to deduce various versions of Hensel's Lemma for polynomials in several additive operators, and to give a criterion for the existence of integration and solutions of certain differential equations on spherically complete valued differential fields, for both valued D-fields in the sense of Scanlon, and differentially valued fields in the sense of Rosenlicht. We modify the approach so that it also covers logarithmic-exponential power series fields. Finally, we give a criterion for a sum of spherically complete subgroups of a valued abelian group to be spherically complete. This in turn can be used to determine elementary properties of power series fields in positive characteristic.     

Boundedly UC Spaces and Topologies on Function Spaces

A new interesting topology on graphs of partial maps is introduced. This topology can be considered as a natural extension to a non locally compact setting of former topologies defined by P. Brandi, R. Ceppitelli and K. Back, having applications in mathematical economics, differential equations and in the convergence of dynamic programming models. New characterizations of boundedly Atsuji spaces are given by the coincidence of and the topology τ _ucb of uniform convergence on bounded sets on C(X,Y) and by topological properties of .      

Lowwner链与复Hilbert空间单位球上推广的Roper-Suffridge算子(Ⅰ)

In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and order α, almost starlikeness of order α, spirallikeness of type of β and starlikeness.