共查询到20条相似文献,搜索用时 0 毫秒
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C. A. Morales 《数学学报(英文版)》2015,31(9):1501-1507
We prove that the existence of positively expansive measures for continuous maps on compact metric spaces implies the existence of e 0 and a sequence of(m, e)-separated sets whose cardinalities go to infinite as m →∞. We then prove that maps exhibiting such a constant e and the positively expansive maps share some properties. 相似文献
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关于Banach空间隐式常微分方程的解的存在性 总被引:3,自引:0,他引:3
林艺 《纯粹数学与应用数学》1999,15(3):68-72
讨论了 Banach 空间中隐式常微分方程 F(t,x,x′) = 0, x(t0 ) = x0 , x′(t0) = y0 的解的存在性,其中, F 的定义域可含无穷远点 相似文献
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Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space. 相似文献
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Nikolaos S Papageorgiou 《Proceedings Mathematical Sciences》1991,101(2):63-70
In this paper we prove some convergence theorems for Banach space valued multifunctions. First we consider the notion of weak
convergence of sets and prove a weak completeness and a weak compactness result of the Dunford-Pettis type for weakly compact,
convex valued integrable multifunctions. Then we consider set valued martingales and establish two convergence theorems. One
using the Kuratowski-Mosco mode of convergence and for the other the Hausdorff mode. 相似文献
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某些局部凸空间上相对弱紧集,相对弱列紧集,相对弱可数紧集的关系 总被引:3,自引:0,他引:3
对可分离的局部凸空间(X,τ),本文建立了相应的局部凸空间(Qx,Tx),利用它证明了当(X,τ)满足某些条件时(赋范空间满足这些条件),EX相对弱紧E相对弱列紧E相对弱可数紧,从而推广了Eberlein等人的工作,证明了在空间D(R ̄n),(R ̄n)和D_(LP),1<p<∞上前述三种弱紧性等价. 相似文献
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We prove in this note that, given a simply connected domainGin the complex plane and a sequence of infinite order linear differential operators generated by entire functions of subexponential type satisfying suitable conditions, then there are holomorphic functionsfonGsuch that the image of any open subset under the action of those operators onfis arbitrarily large. This generalizes an earlier result about images of derivatives. A known statement about close orbits is also strengthened. 相似文献
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Khodr Shamseddine 《Journal of Mathematical Analysis and Applications》2010,368(1):281-292
Two topologies on the Levi-Civita field R will be studied: the valuation topology induced by the order on the field, and another weaker topology induced by a family of seminorms, which we will call weak topology. We show that each of the two topologies results from a metric on R, that the valuation topology is not a vector topology while the weak topology is, and that R is complete in the valuation topology while it is not in the weak topology. Then the properties of both topologies will be studied in details; in particular, we give simple characterizations of open, closed, and compact sets in both topologies. 相似文献
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《Applied Mathematics Letters》2012,25(3):429-433
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied by Du (2010) [14] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper, we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable, prove a completion theorem, and also obtain some more results in topological vector space valued cone normed spaces. 相似文献
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We show that the unit ball of in its weak topology is a continuous image of , and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when is uncountable.
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Gerald Beer 《Set-Valued Analysis》1999,7(3):195-208
Many years ago, S.-T. Hu gave necessary and sufficient conditions for a family of subsets of a metrizable space X to be the family of bounded sets for some admissible metric for the space. In this article, we show that in any noncompact metrizable space there are uncountably many distinct metric boundedness structures. Also, given an initial metric d for X, we look carefully at the problem of characterizing those boundedness structures determined by metrics uniformly equivalent to d. Applications to hyperspaces are given. Throughout, we rely on a dual approach to the study of metric boundedness. 相似文献
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Bo-Yong Chen 《Proceedings of the American Mathematical Society》2006,134(1):139-148
We prove a localization principle of the Bergman kernel form and metric for pseudoconvex domains in the complex projective space. An estimate of the Bergman distance is also given.
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M. V. Balashov 《Mathematical Notes》2002,71(3-4):295-304
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Camillo Costantini 《Proceedings of the American Mathematical Society》1998,126(11):3393-3396
We prove the following two results. 1) There exists a non-separable complete metric space whose Wijsman hypertopology is not Cech-complete. 2) There exist a non-separable metrizable space and two compatible metrics on it, such that the collections of the Borel sets generated by the relative Wijsman hypertopologies do not coincide.
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Fulton and MacPherson (Ann. Math. 139 (1994) 183) found a Sullivan dg-algebra model for the space of n-configurations of a smooth complex projective variety X. K?í? (Ann. Math. 139 (1994) 227) gave a simpler model, En(H), depending only on the cohomology ring, H?H*X.We construct an even simpler and smaller model, Jn(H). We then define another new dg-algebra, En(H°), and use Jn(H) to prove that En(H°) is a model of the space of n-configurations of the non-compact punctured manifold X°, when X is 1-connected. Following an idea of Drinfel’d (Leningrad Math. J. 2 (1991) 829), we put a simplicial bigraded differential algebra structure on {En(H°)}n?0. 相似文献
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In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain. 相似文献
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Geometric aspects of the moduli space of Riemann surfaces 总被引:10,自引:0,他引:10
Shing-Tung Yau 《中国科学A辑(英文版)》2005,48(Z1)
We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford. 相似文献