共查询到20条相似文献,搜索用时 31 毫秒
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Feng Tan 《Topology and its Applications》2011,158(3):533-541
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Consider the surjective, continuous map f:X→X and the continuous map of K(X) into itself induced by f, where X is a compact metric space and K(X) is the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper we give examples showing that sensitivity of f does not imply sensitivity of . Furthermore, we prove that if f is a surjective, continuous interval map, then is sensitive if and only if f is sensitive. 相似文献
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For a metric continuum X, we consider the hyperspaces X2 and C(X) of the closed and nonempty subsets of X and of subcontinua of X, respectively, both with the Hausdorff metric. For a given map we investigate the transitivity of the induced maps and . Among other results, we show that if X is a dendrite or a continuum of type λ and is a map, then C(f) is not transitive. However, if X is the Hilbert cube, then there exists a transitive map such that f2 and C(f) are transitive. 相似文献
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Vegard Lima 《Journal of Functional Analysis》2004,210(1):148-170
We prove that a Banach space X has the metric approximation property if and only if , the space of all finite rank operators, is an ideal in , the space of all bounded operators, for every Banach space Y. Moreover, X has the shrinking metric approximation property if and only if is an ideal in for every Banach space Y.Similar results are obtained for u-ideals and the corresponding unconditional metric approximation properties. 相似文献
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Jean Saint Raymond 《Topology and its Applications》2007,154(8):1714-1725
The aim of this note is to prove the following result: “Assume that X is a metric Borel space of class ξ, that is continuous, that every fiber f−1(y) is complete and that every countable compact subset of Y is the image by f of some compact subset of X. Then Y is Borel and moreover of class ξ”. We give also an extension to the case where the fibers are only assumed to be Polish. 相似文献
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Gábor Bodnár 《Journal of Pure and Applied Algebra》2003,179(3):221-233
Given a birational projective morphism of quasi-projective varieties . We want to find the ideal sheaf over X such that the blowing up of X along corresponds to f. In this paper we approach the problem from two directions, solving two subcases. First we present a method that determines when f is the composition of blowing ups along known centers, then by another method, we compute directly from . 相似文献
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Let f, g be entire functions. If there exist M1,M2>0 such that |f(z)|?M1|g(z)| whenever |z|>M2 we say that f?g. Let X be a reproducing Hilbert space with an orthogonal basis . We say that X is an ordered reproducing Hilbert space (or X is ordered) if f?g and g∈X imply f∈X. In this note, we show that if then X is ordered; if then X is not ordered. In the case , there are examples to show that X can be of order or opposite. 相似文献
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Yves Félix 《Topology》2007,46(5):493-506
In the rational category of nilpotent complexes, let E be an H-space acting on a space X. With mild hypotheses we show that the action on the base point factors through a map ΓE:SE→X, where SE is a finite product of odd-dimensional spheres and ΓE is a homotopy monomorphism. Among others, the following consequences are obtained: if and only if is essential and if and only if X satisfies a strong splitting condition. 相似文献
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We give a characterization of exponentiable monomorphisms in the categories of ω-complete posets, of directed complete posets and of continuous directed complete posets as those monotone maps f that are convex and that lift an element (and then a queue) of any directed set (ω-chain in the case of ) whose supremum is in the image of f (Theorem 1.9). Using this characterization, we obtain that a monomorphism f:X→B in (, ) exponentiable in w.r.t. the Scott topology is exponentiable also in (, ). We prove that the converse is true in the category , but neither in , nor in . 相似文献
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Piotr Niemiec 《Topology and its Applications》2008,155(12):1323-1328
The aim of the paper is to generalize the notion of the Haar integral. For a compact semigroup S acting continuously on a Hausdorff compact space Ω, the algebra A(S)⊂C(Ω,R) of S-invariant functions and the linear space M(S) of S-invariant (real-valued) finite signed measures are considered. It is shown that if S has a left and right invariant measure, then the dual space of A(S) is isometrically lattice-isomorphic to M(S) and that there exists a unique linear operator (called the Haar integral) such that for each f∈A(S) and for any f∈C(Ω,R) and s∈S, , where . 相似文献
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Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γk(G), the connected k-domination number ; the k-independent domination number and the k-irredundance number irk(G). The authors prove that if an irk-set X is a k-independent set of G, then , and that for k?2, if irk(G)=1, if irk(G) is odd, and if irk(G) is even, which generalize some known results. 相似文献
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Elmas Irmak 《Topology》2004,43(3):513-541
Let S be a closed, connected, orientable surface of genus at least 3, be the complex of curves on S and be the extended mapping class group of S. We prove that a simplicial map, , preserves nondisjointness (i.e. if α and β are two vertices in and i(α,β)≠0, then i(λ(α),λ(β))≠0) iff it is induced by a homeomorphism of S. As a corollary, we prove that if K is a finite index subgroup of and is an injective homomorphism, then f is induced by a homeomorphism of S and f has a unique extension to an automorphism of . 相似文献
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Karim Samei 《Journal of Pure and Applied Algebra》2007,209(3):813-821
In this paper the zero-divisor graph Γ(R) of a commutative reduced ring R is studied. We associate the ring properties of R, the graph properties of Γ(R) and the topological properties of . Cycles in Γ(R) are investigated and an algebraic and a topological characterization is given for the graph Γ(R) to be triangulated or hypertriangulated. We show that the clique number of Γ(R), the cellularity of and the Goldie dimension of R coincide. We prove that when R has the annihilator condition and ; Γ(R) is complemented if and only if is compact. In a semiprimitive Gelfand ring, it turns out that the dominating number of Γ(R) is between the density and the weight of . We show that Γ(R) is not triangulated and the set of centers of Γ(R) is a dominating set if and only if the set of isolated points of is dense in . 相似文献
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Steve Seif 《Journal of Pure and Applied Algebra》2008,212(5):1162-1174
A classic result from the 1960s states that the asymptotic growth of the free spectrum of a finite group is sub-log-exponential if and only if is nilpotent. Thus a monoid is sub-log-exponential implies , the pseudovariety of semigroups with nilpotent subgroups. Unfortunately, little more is known about the boundary between the sub-log-exponential and log-exponential monoids.The pseudovariety consists of those finite semigroups satisfying (xωyω)ω(yωxω)ω(xωyω)ω≈(xωyω)ω. Here it is shown that a monoid is sub-log-exponential implies . A quick application: a regular sub-log-exponential monoid is orthodox. It is conjectured that a finite monoid is sub-log-exponential if and only if it is , the finite monoids in having nilpotent subgroups. The forward direction of the conjecture is proved; moreover, the conjecture is proved for when is completely (0)-simple. In particular, the six-element Brandt monoid (the Perkins semigroup) is sub-log-exponential. 相似文献
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Let G be a graph and for any natural number r, denotes the minimum number of colors required for a proper edge coloring of G in which no two vertices with distance at most r are incident to edges colored with the same set of colors. In [Z. Zhang, L. Liu, J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett. 15 (2002) 623-626] it has been proved that for any tree T with at least three vertices, . Here we generalize this result and show that . Moreover, we show that if for any two vertices u and v with maximum degree d(u,v)?3, then . Also for any tree T with Δ(T)?3 we prove that . Finally, it is shown that for any graph G with no isolated edges, . 相似文献
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Fangyan Lu 《Journal of Mathematical Analysis and Applications》2003,284(1):127-143
Let X be a real or complex Banach space. Let and be two nest algebras on X. Suppose that φ is an additive bijective mapping from onto such that φ(A2)=φ(A)2 for every . Then φ is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either φ(A)=TAT−1 for every or φ(A)=TA∗T−1 for every . 相似文献
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P. Shvartsman 《Journal of Functional Analysis》2004,210(1):1-42
Let F be a mapping from a metric space into the family of all m-dimensional affine subsets of a Banach space X. We present a Helly-type criterion for the existence of a Lipschitz selection f of the set-valued mapping F, i.e., a Lipschitz continuous mapping satisfying . The proof of the main result is based on an inductive geometrical construction which reduces the problem to the existence of a Lipschitz (with respect to the Hausdorff distance) selector SX(m) defined on the family of all convex compacts in X of dimension at most m. If X is a Hilbert space, then the classical Steiner point of a convex body provides such a selector, but in the non-Hilbert case there is no known way of constructing such a point. We prove the existence of a Lipschitz continuous selector for an arbitrary Banach space X. The proof is based on a new result about Lipschitz properties of the center of mass of a convex set. 相似文献
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For any numerical function we give sufficient conditions for resolving the controlled extension problem for a closed subset A of a normal space X. Namely, if the functions , and satisfy the equality E(f(a),g(a))=h(a), for every a∈A, then we are interested to find the extensions f? and ? of f and g, respectively, such that , for every x∈X. We generalize earlier results concerning E(u,v)=u·v by using the techniques of selections of paraconvex-valued LSC mappings and soft single-valued mappings. 相似文献