共查询到18条相似文献,搜索用时 109 毫秒
1.
2.
由导集运算定义拓扑的方法 总被引:1,自引:0,他引:1
对点集拓扑学中由导集运算决定拓扑的方法进行了讨论,主要结果是,设X是一个集合,d*:P(X)→P(X)是集值映射,若d*满足:A,B∈P(X),(1)d*()=,(2)d*(A∪B)=d*(A)∪d*(B),(3)d*(d*(A))A∪d*(A),(4)d*(A)={x∈X x∈d*(A-{x})},则存在X的唯一拓扑T,使得在拓扑空间(X,T)中,A∈P(X),d(A)=d*(A). 相似文献
3.
4.
5.
运用连续值逻辑语义的方法研究fuzzifying拓扑空间,从Pre-开集出发引入了Pre-导集的概念,并且给出了它的一些性质,进一步探讨了Pre-网收敛理论.这些研究有助于丰富和发展fuzzifying拓扑学的基本理论. 相似文献
6.
本文扩展了普通集X的导算子d的定义,诱导出了X的fuzzy导算子d,进而由~^d诱导出了X的一个fuzzy拓扑T,证明了fuzzy拓扑空间(X,T)愉是由d诱导的分明拓扑空间(X,π)拓扑生成的,对X的每个fuzzy导算子d,存在X唯一拓扑T,使得对X的每个fuzzy子集A,其在(X,T)中的导集A^d恰是它在fuzzy导算子~^d下的象~^d(A)。 相似文献
7.
L—fts中的导集和导算子 总被引:1,自引:1,他引:0
本文首先讨论了L-fts中LF集的聚点的分布;其次讨论了LF集的导集的一些性质,并给出了一般的L-fts中类似于杨忠道定理的结果;本文最后引进了导算子的概念,并用其刻划一般的L-fts。 相似文献
8.
L─fts中的导集和导算子 总被引:1,自引:0,他引:1
本文首先讨论了L─fts中LF集的聚点的分布;其次讨论了LF集的导集的一些性质,并给出了一般的L─fts中类似于杨忠道定理的结果;本文最后引进了导算子的概念,并用其刻划一般的L─fts. 相似文献
9.
本文把点集拓扑学中的C·T·Yang定理推广到模糊拓扑学中 ,并且获得了一些其它新的结果 相似文献
10.
在拓扑空间中, 在$G$方法意义下以$G$壳与$G$核为基础, 引入$G$壳闭集,$G$核开集,$G$核邻域与$G$核导集的概念, 讨论其相应的一些性质. 特别的, 定义了点式$G$方法, 提供了在此方法下$G$闭集与$G$壳闭集, $G$开集与$G$核开集, $G$邻域与$G$核邻域, $G$导集与$G$核导集的一致性, 丰富了拓扑空间中关于$G$闭集, $G$开集, $G$内部, $G$邻域和$G$导集的一些结果. 同时, 提出一些问题以供进一步研究. 相似文献
11.
本文首先研究由经典拓扑诱导的导算子的性质,给出其分解定理;其次用该诱导导算 子给出格值上(下)半连续函数的若干刻画条件. 相似文献
12.
13.
M. Putinar 《Numerische Mathematik》2002,93(1):131-152
Summary A special type diagonal Padé approximation for a class of hermitian power series in two variables is related to a canonical
strong-operator topology, finite-rank approximation of cyclic operators. The expected convergence of the process (uniform
or in measure) is derived from operator theory facts.
Paper partially supported by the National Science Foundation Grant DMS-9800666 相似文献
14.
15.
Ronald K. Perline 《Numerical Functional Analysis & Optimization》2013,34(11-12):1139-1175
The continuity and differentiability for integral operator in Banach spaces are proved with respect to Lp–topology. The weak normal integrand is defined, so that a generalized measurable selection theorem is derived, and the conjugate functional for integral functional is formulated. The duality theorem of optimization problem for integral functional is established by using the conjugate functional. 相似文献
16.
We show that every bounded linear operator on a separable, infinite-dimensional Hilbert space H is the sum of two operators in the norm-closure of the set of operators on H that are chaotic in the sense of Devaney. We also observe that the density of several classes of cyclic operators, with respect to the strong operator topology, may be derived from a result by Hadwin et al. (Proc Amer. Math. Soc. 76 (1979) 250-252). 相似文献
17.
Abbas Edalat 《Topology and its Applications》2010,157(9):1629-1650
We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak∗ compact and convex valued maps equipped with the Scott topology, is continuous. For finite dimensional Euclidean spaces, where the L-derivative and the Clarke gradient coincide, we provide a simple characterization of the basic open subsets of the L-topology. We use this to verify that the L-topology is strictly coarser than the well-known Lipschitz norm topology. A complete metric on Lipschitz maps is constructed that is induced by the Hausdorff distance, providing a topology that is strictly finer than the L-topology but strictly coarser than the Lipschitz norm topology. We then develop a fundamental theorem of calculus of second order in finite dimensions showing that the continuous integral operator from the continuous Scott domain of non-empty convex and compact valued functions to the continuous Scott domain of ties is inverse to the continuous operator induced by the L-derivative. We finally show that in dimension one the L-derivative operator is a computable functional. 相似文献
18.
A. M. Bikchentaev 《Doklady Mathematics》2018,98(3):545-548
For a von Neumann algebra with a faithful normal semifinite trace, the properties of operator “intervals” of three types for operators measurable with respect to the trace are investigated. The first two operator intervals are convex and closed in the topology of convergence in measure, while the third operator interval is convex for all nonnegative operators if and only if the von Neumann algebra is Abelian. A sufficient condition for the operator intervals of the second and third types not to be compact in the topology of convergence in measure is found. For the algebra of all linear bounded operators in a Hilbert space, the operator intervals of the second and third types cannot be compact in the norm topology. A nonnegative operator is compact if and only if its operator interval of the first type is compact in the norm topology. New operator inequalities are proved. Applications to Schatten–von Neumann ideals are obtained. Two examples are considered. 相似文献