共查询到20条相似文献,搜索用时 46 毫秒
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如果拓扑空间X,Y的拓扑和X∨Y的自同伦等价可以对角化,则X∨Y的自同伦等价群Aut(X∨Y)可表示为它的两个子群Autx(X∨Y)与AutY(X∨y)的乘积. 相似文献
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李祖泉 《纯粹数学与应用数学》2005,21(2):154-157
应用k-网的概念证明了:若X,Y为(ξ)0空间且Y为局部紧的,则X到Y上满足条件(G)的点紧致的族连续集值映射族依紧开拓扑是(ξ)0空间. 相似文献
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研究拓扑偶范畴中的自同伦等价群.对于同伦可结合与同伦可逆的Co-H空间X与Y,我们将在一定的条件下得到一条可裂的短正合序列:1→(?)(X)→(?)(X(?)Y)→(?)(Y)→1. 相似文献
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集值映射空间在紧开拓扑下的NO性质 总被引:3,自引:0,他引:3
本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若X,Y为NO空间,则X到Y上的点紧致的连续集值映射族依紧开拓扑是NO空间,从而将Michael[1]的结论推广到更大的映射空间类上. 相似文献
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本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若X,Y为N_0空间,则X到Y上的点紧致的连续集值映射族依紧开拓扑是N_0空间,从而将Michael的结论推广到更大的映射空间类上. 相似文献
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在L-拓扑空间中引入半Sβ-紧性,这种紧性是针对任意L-模糊子集定义的,它是Sβ-紧性的推广。研究半Sβ-紧性的性质,如一个半Sβ-紧集与一个半闭集的交仍为半Sβ-紧的;半Sβ-紧性在不定映射下保持不变;由分明拓扑空间(X,τ)拓扑生成的L-拓扑空间(LX,ωL(τ))是半Sβ-紧的当且仅当(X,τ)是半紧的。此外,还给出了半Sβ-紧性的网式刻画。 相似文献
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设X是桶空间,Y是序列完备的局部凸空间.本文证明了,由X到Y的紧算子组成的算子级数,其在弱算子拓扑下和一致算子拓扑下的子级数收敛是一致的,当且仅当(X’,β(X’,X))不拓扑同胚地包含CO;同时证明了,N’中σ(X’,X)-子级数收敛级数是β(X’;X)-子级数收敛的,当且仅当(X’,β(X’,X))不拓扑同胚地包含CO. 相似文献
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Martín H. Escard 《Topology and its Applications》2002,120(3):21-463
If X and Y are Hausdorff spaces with X locally compact, then the compact-open topology on the set C(X,Y) of continuous maps from X to Y is known to produce the right function-space topology. But it is also known to fail badly to be locally compact, even when Y is locally compact. We show that for any Tychonoff space Y, there is a densely injective space Z containing Y as a densely embedded subspace such that, for every locally compact space X, the set C(X,Z) has a compact Hausdorff topology whose relative topology on C(X,Y) is the compact-open topology. The following are derived as corollaries: (1) If X and Y are compact Hausdorff spaces then C(X,Y) under the compact-open topology is embedded into the Vietoris hyperspace V(X×Y). (2) The space of real-valued continuous functions on a locally compact Hausdorff space under the compact-open topology is embedded into a compact Hausdorff space whose points are pairs of extended real-valued functions, one lower and the other upper semicontinuous. The first application is generalized in two ways. 相似文献
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In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset. 相似文献
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Abolfazl Tarizadeh 《代数通讯》2019,47(1):195-205
In this article, a new and natural topology on the prime spectrum is introduced, which behaves completely as the dual of the Zariski topology. It is called the flat topology. The basic and also some sophisticated properties of the flat topology are proved. Specially, various algebraic characterizations for the noetherianess of the flat topology are given. Using the flat topology, then some facts on the structure of the prime ideals of a ring come to light which are not in the access of the Zariski topology. 相似文献
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Sen ZhuZhi-Hao Ma 《Applied Mathematics Letters》2012,25(3):631-635
In this paper, we study the interval topology on effect algebras, and prove that effect algebra operation on Hilbert space effect algebra E(H) is not jointly continuous under the interval topology. 相似文献
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Farid Bahrami 《Journal of Mathematical Analysis and Applications》2008,344(2):857-868
In this paper we will introduce two other topologies, coarser than the so-called strong topology, on a class of Šerstnev probabilistic normed spaces, and obtain some important properties of these topologies. We will show that under the first topology, denoted by τ0, our probabilistic normed space is decomposable into the topological direct sum of a normable subspace and the subspace of probably null elements. Under the second topology, which is in fact the inductive limit topology of a family of locally convex topologies, the dual space becomes a locally convex topological vector space. 相似文献
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On the supercyclicity and hypercyclicity of the operator algebra 总被引:1,自引:0,他引:1
Let B(X) be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or *-strong topology. We give sufficient conditions for a continuous linear mapping L : B(X) →B(X) to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied' by Chan and here we obtain an analogous result in the case of *-strong operator topology. 相似文献
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This paper mainly focuses on pinning synchronization of directed networks under disconnected switching topology. Firstly, by introducing the uniformly directed spanning tree on average (UDSTA) for a time-varying digraph and designing a switching pinning controller, the asymptotic synchronization of complex networks with large number of switching topologies is investigated, in which strong connectivity and structural balance for switching topology are no longer required. Furthermore, a class of almost-period (AP) switching mode is introduced. By means of matrix decomposition, the pinning synchronization criteria of complex networks under AP switching topology are derived and the pinning nodes are selected according to maximal strongly connected root-subgraphs (MSCRSs) of average topology. Finally, a type of coupled neural networks with numerical simulations is introduced to illustrate the theoretical results. 相似文献
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Antonio M. Peralta Ignacio Villanueva J.D. Maitland Wright Kari Ylinen 《Journal of Mathematical Analysis and Applications》2007,325(2):968-974
Let X be a Banach space. Then there is a locally convex topology for X, the “Right topology,” such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the “Right” topology, into Y equipped with the norm topology. When T is only sequentially continuous with respect to the Right topology, it is said to be pseudo weakly compact. This notion is related to Pelczynski's Property (V). 相似文献
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Pratulananda Das 《Fuzzy Sets and Systems》1998,100(1-3):367-372
The notion of product fuzzy topology in the case of fuzzy topology on fuzzy sets is introduced and the product invariance of fuzzy Hausdorffness, compactness, connectedness are examined. The product fuzzy topology is used to define fuzzy group topology on a fuzzy subgroup of a group G and some properties of fuzzy topological groups are obtained. 相似文献
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Dikran Dikranjan Anna Giordano Bruno 《Topology and its Applications》2011,158(17):2391-2407
In the general context of functorial topologies, we prove that in the lattice of all group topologies on an abelian group, the infimum between the Bohr topology and the natural topology is the profinite topology. The profinite topology and its connection to other functorial topologies is the main objective of the paper. We are particularly interested in the poset C(G) of all finite-index subgroups of an abelian group G, since it is a local base for the profinite topology of G. We describe various features of the poset C(G) (its cardinality, its cofinality, etc.) and we characterize the abelian groups G for which C(G)?{G} is cofinal in the poset of all subgroups of G ordered by inclusion. Finally, for pairs of functorial topologies T, S we define the equalizer E(T,S), which permits to describe relevant classes of abelian groups in terms of functorial topologies. 相似文献