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For a Tychonoff space X , we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelöf Σ-property of X in terms of Cp(X), we extend Okunev?s results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then υY is a Lindelöf Σ-space (respectively K-analytic) if υX has this property. In the second part, applying Christensen?s theorem, we extend Pelant?s result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space. We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by ?p-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and ?p-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented. 相似文献
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We create a new, functional calculus, approach to approximation formulas for C0-semigroups on Banach spaces restricted to the domains of fractional powers of their generators. This approach allows us to equip the approximation formulas with rates which appear to be optimal in a natural sense. In the case of analytic semigroups, we improve our general results obtaining better convergence rates which are optimal in that case too. The setting of analytic semigroups includes also the case of convergence on the whole space. As an illustration of our approach, we deduce optimal convergence rates in classical approximation formulas for C0-semigroups restricted to the domains of fractional powers of their generators. 相似文献
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It is well-known that the coordinator polynomials of the classical root lattice of type An and those of type Cn are real-rooted. They can be obtained, either by the Aissen–Schoenberg–Whitney theorem, or from their recurrence relations. In this paper, we develop a trigonometric substitution approach which can be used to establish the real-rootedness of coordinator polynomials of type Dn. We also find the coordinator polynomials of type Bn are not real-rooted in general. As a conclusion, we obtain that all coordinator polynomials of Weyl group lattices are log-concave. 相似文献
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A hypergraph is called an r×rgrid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e., a family of sets {A1,…,Ar,B1,…,Br} such that Ai∩Aj=Bi∩Bj=0? for 1≤i<j≤r and |Ai∩Bj|=1 for 1≤i,j≤r. Three sets C1,C2,C3 form a triangle if they pairwise intersect in three distinct singletons, |C1∩C2|=|C2∩C3|=|C3∩C1|=1, C1∩C2≠C1∩C3. A hypergraph is linear , if |E∩F|≤1 holds for every pair of edges E≠F. 相似文献
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Spencer Dowdall Ilya Kapovich Christopher J. Leininger 《Comptes Rendus Mathematique》2014,352(11):885-887
A result of Handel–Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group FN and its inverse is bounded by a constant CN. In this short note, we show that this constant CN cannot be chosen independent of the rank N. 相似文献
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For a space X denote by Cb(X) the Banach algebra of all continuous bounded scalar-valued functions on X and denote by C0(X) the set of all elements in Cb(X) which vanish at infinity. 相似文献
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We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices, X1,…,Xn are pointed connected CW-complexes and CXi is the cone on Xi, then the polyhedral product determined by K and the pairs (CXi,Xi) is homotopy equivalent to a wedge of suspensions of smashes of the Xi’s. Earlier work of the authors dealt with the special case where each Xi is a loop space. New techniques are introduced to prove the general case. These have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes. We discuss connections between polyhedral products and toric topology, combinatorics, and classical homotopy theory. 相似文献
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Let K be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K) and C0(K), the class of left translation invariant w?-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C?-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w?-subalgebras of L∞(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C?-subalgebras of C0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L∞(K) and C0(K). 相似文献
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We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X is monotonically retractable if and only if Cp(X) is monotonically Sokolov. Besides, a space X is monotonically Sokolov if and only if Cp(X) is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R-quotient images and Fσ-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X and Cp(X) are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X such that Cp(X) has the Lindelöf Σ-property but neither X nor Cp(X) is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov. 相似文献
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It is proved that the cookie-cutter set in R is structurally instable in C1 topology, that means for the invariant set E of the IFS {fi}i, we can always perturb {fi}i arbitrarily small in C1 topology to provide an IFS {gi}i with its invariant set F, such that dimHE=dimHF and E,F are not Lipschitz equivalent. 相似文献
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Let X be a completely regular Hausdorff space and Cb(X) be the Banach space of all real-valued bounded continuous functions on X, endowed with the uniform norm. It is shown that every weakly compact operator T from Cb(X) to a quasicomplete locally convex Hausdorff space E can be uniquely decomposed as T=T1+T2+T3+T4, where Tk:Cb(X)→E(k=1,2,3,4) are weakly compact operators, and T1 is tight, T2 is purely τ -additive, T3 is purely σ -additive and T4 is purely finitely additive. Moreover, we derive a generalized Yosida–Hewitt decomposition for E-valued strongly bounded regular Baire measures. 相似文献
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Qi Duan Huanling Zhang Yunfeng Zhang E.H. Twizell 《Journal of Computational and Applied Mathematics》2007
This paper deals with the approximation properties of a kind of rational spline with linear denominator when the function being interpolated is C3 in an interpolating interval. Error estimate expressions of interpolating functions are derived, convergence is established, the optimal error coefficient, ci, is proved to be symmetric about the parameters of the rational interpolation and it is bounded. Finally, the precise jump measurements of the second derivatives of the interpolating function at the knots are given. 相似文献