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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. 相似文献
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设(X,τ)是一个拓扑空间。在本文中,我们证明了在超空间2X上局部有限拓扑eτ与局部有限覆盖拟一致uLF所导出的超拓扑|2uLF|是相同的。我们还证明了下面条件是等价的:(1)(X,τ)是仿紧的;(2)(X,τ)是orth紧的,且eτ=|2uFT|;(3)存在一个Lebes-yue拟一致uL,使eτ< 相似文献
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李金金 《纯粹数学与应用数学》2014,(1):60-68
设(X,d,f)为拓扑动力系统,其中X为局部紧可分的可度量化空间,d为紧型度量,f为完备映射,用2X表示由X的所有非空闭子集构成的集族,(2X,ρ,2f)为由(X,d,f)所诱导的赋予hit-or-miss拓扑的超空间动力系统.本文引入了余紧点传递和弱拓扑传递的定义.特别的,在X满足一定的条件时,给出了点传递,弱拓扑传递和余紧点传递之间的关系,并研究了(X,d,f)的余紧传递点,回复点和几乎周期点分别与(2X,ρ,2f)的传递点,回复点和几乎周期点之间的蕴含关系.这些结论丰富了赋予hit-or-miss拓扑的超空间的研究内容. 相似文献
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诱导I-Fuzzy拓扑空间 总被引:2,自引:0,他引:2
本文引入了生成I-Fuzzy拓扑空间的概念,研究了Fuzzifying拓扑空间(X,τ)与其相应的生成I-Fuzzy拓扑空间(IX,ω(τ))的联系;然后介绍了ω,ι算子及它们的运算性质;最后给出并研究了I-Fuzzy诱导空间,I-Fuzzy弱诱导空间,I-Fuzzy满层空间的定义和它们间的联系. 相似文献
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L-fuzzy拓扑空间的弱诱导化 总被引:4,自引:0,他引:4
对任一L-fuzzy拓扑空间,本文给出了两个与之密切相关的弱诱导空间,从而证明了弱诱导空间范畴是一般fuzzy拓扑空间范畴的反射和余反射满子范畴.特别地我们较详细地讨论了次T_o完全正则空间的弱诱导化. 相似文献
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设(X,d,f)为拓扑动力系统,其中X为局部紧第二可数Hausdorff空间,d为紧型度量,f为完备映射,用2^x和f分别表示由X的所有非空闭子集和所有闭子集构成的集族,(2^x,ρ,2^f)和(f,ρ,2^f)为由(X,d,f)诱导的赋予hit—or—miss拓扑的超空间动力系统.本文研究了h(X,d,f)和h(2^... 相似文献
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本文研究L-fuzzy 拓扑空间的一类几乎开L-fuzzy 集的性质,在L-fuzzy 拓扑空间中引入了α-结构的概念,证明了由一般拓扑空间(X,T)诱导的L-fuzzy 拓扑空间(LX,WL(T))的α-结构必是LX 上的L-fuzzy 拓扑,并且指出这个拓扑就是由一般拓扑空间(X,T)的α- 结构诱导的.此外,本文还给出了与诱导的L-fuzzy拓扑空间的α-结构相关的若干性质. 相似文献
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Certain topological properties of the hyperspaces have been studied in [1], [2]and[3]. In this paper we will discuss some topological properties of hyperspace[,2~T], and will generalize related results of Z. Michael [1], A. Frank, Chimenti,[2],寿纪麟[4]. 相似文献
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给出序列伪轨跟踪性的定义,得到拓扑可迁的一个充分条件,并证明,若f是同胚,则f具有序列伪轨跟踪性当且仅当其逆极限空间上的移位映射σf具有序列伪轨跟踪性。 相似文献
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Hans-Jürgen Schmidt 《Mathematische Nachrichten》1984,118(1):115-122
In the hyperspace Exp X of all closed subsets of a topological space X interval and order topology solely use the ?-relation in Exp X for their definitions whereas HAUSDORFF set convergence and VIETORIS topology use neighbourhoods in X itself. Nevertheless there exist intimate but non-trivial relations between them. 相似文献
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Hans-Jürgen Schmidt 《Mathematische Nachrichten》1984,118(1):105-113
The hyperspace of all nonvoid closed subsets of a topological space will be topologized by means of different methods; each of them generalizes known definitions of special hyperspace topologies. One method uses the VIETORIS topology in the hyperspaces of certain extension spaces. Another one uses certain systems of closed subsets and leads to just the same class of hyperspace topologies. In natural order VIETORIS topology is the supremum of this class, and for locally compact spaces FLACHSMEYER topology is the infimum of this class. 相似文献
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Alexander M. Sokhet 《Monatshefte für Mathematik》1999,97(2):61-82
Let H be a closed normal subgroup of a locally compact separable group G, and suppose that H acts ergodically on a Lebesgue space. If both the given H-action and the natural G-action on G/H have funny rank one, then the induced G-action has it also. For G solvable, the second condition is always true. A similar (but easier) theorem is also true for approximately transitive actions, even without the normality assumption on H. 相似文献
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Alexander M. Sokhet 《Monatshefte für Mathematik》1999,128(1):61-82
Let H be a closed normal subgroup of a locally compact separable group G, and suppose that H acts ergodically on a Lebesgue space. If both the given H-action and the natural G-action on G/H have funny rank one, then the induced G-action has it also. For G solvable, the second condition is always true. A similar (but easier) theorem is also true for approximately transitive actions,
even without the normality assumption on H.
Received 23 February 1998 相似文献
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The topological r-entropy and measure theoretic r-entropy of a flow are studied. For a flow(X, φ), it is shown that topological(measure theoretic) r-entropy is equal to the topological(measure theoretic) entropy of the time one map φ1 as r decreases to zero. The Brin–Katok’s entropy formula for r-entropy is also established. 相似文献