共查询到20条相似文献,搜索用时 62 毫秒
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本文研究了狭义拟仿紧空间的两个因子的乘积和逆序列的极限的性质,还肯定地回答了刘应明在[1,2]中提出的一个问题。 相似文献
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朱培勇 《数学年刊A辑(中文版)》2001,(3)
本文主要证明了如下一些结果:(1)设X=Lim并且每个投射πσ是开满映射,如果X是-仿紧的且每个 Xσ是正规狭义拟仿紧的,则 X是正规狭义拟仿紧的;如果 X是遗传-仿紧的且每个 Xσ是遗传正规狭义拟仿紧的.则 X是遗传正规狭义拟仿紧的. (2)如果 X=是 -仿紧空间,则X是正规狭义拟仿紧的当且仅当 是正规狭义拟仿紧的.最后,还给出了诸多覆盖性质的可数乘积的一个等价性命题. 相似文献
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利用算子半群生成元的边界扰动方法,给出了Banach格上C0半群的拟紧性和不可约性的充分条件.并利用该结果对一串联可修复系统的拟紧性和不可约性进行了研究. 相似文献
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L—Fuzzy拓扑空间的仿紧性和强仿紧性 总被引:2,自引:1,他引:1
仿紧性是分明拓扑学中的一个重要概念,如何合理定义LF拓扑中的仿紧性是一引人注目的课题。基于良紧性的几何刻划[4],文[3]和文[2]分别引入F拓扑中的局部有限族和仿紧性。文[2]对弱诱导的仿紧空间进行了比较深入的研究。但[2]和[3]的讨论还没有涉及到仿紧性的可乘性、分离性等问题。此外[2]引入了另一种局部有限性质: 相似文献
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In this paper,we present that if Y is a hereditarily metacompact space and{Xn:n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent:(1)Y×∏n∈ωXn is metacompact,(2)Y×∏n∈ωXn is countable metacompact,(3)Y×n∈ωXn is orthocompact.Thereby,this result generalizes Theorem 5.4 in[Tanaka,Tsukuba.J.Math.,1993,17:565–587].In addition,we obtain that if Y is a hereditarilyσ-metacompact space and{Xn:n∈ω∏}is a countable collection of Cech-scatteredσ-metacompact spaces,then the product Y×n∈ωXn isσ-metacompact. 相似文献
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In this note, we show that each fragmentable space introduced by Jayne and Rogers in 1985 is of class which was introduced by Kenderov in 1984. Our example shows that a space which is of class may not be a fragmentable space.
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In this paper (weakly) separating maps between spaces of bounded continuous functions over a nonarchimedean field are studied. It is proven that the behaviour of these maps when is not locally compact is very different from the case of real- or complex-valued functions: in general, for -compact spaces and , the existence of a (weakly) separating additive map implies that and are homeomorphic, whereas when dealing with real-valued functions, this result is in general false, and we can just deduce the existence of a homeomorphism between the Stone-Cech compactifications of and . Finally, we also describe the general form of bijective weakly separating linear maps and deduce some automatic continuity results.
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Harold Bell Wlodzimierz Bryc 《Proceedings of the American Mathematical Society》2001,129(7):2119-2125
Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational ``rate function" representation.
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We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.
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Two examples are given that answer in the negative the following question asked by E. M. Bator: If is bounded and weakly measurable and for each in there is a bounded sequence in such that a.e., does it follow that is Pettis integrable?
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J. Hagler 《Proceedings of the American Mathematical Society》2002,130(11):3313-3324
Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .
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It is shown that a separable Banach space can be given an equivalent norm with the following properties: If is relatively weakly compact and , then converges in norm. This yields a characterization of reflexivity once proposed by V.D. Milman. In addition it is shown that some spreading model of a sequence in is 1-equivalent to the unit vector basis of (respectively, ) implies that contains an isomorph of (respectively, ).
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The $\mathbb{Z}_{+}$-ring is an important invariant in the theory of tensor category. In this paper, by using matrix method, we describe all irreducible $\mathbb{Z}_{+}$-modules over a $\mathbb{Z}_{+}$-ring $\mathcal{A}$, where $\mathcal{A}$ is a commutative ring with a $\mathbb{Z}_{+}$-basis{$1$, $x$, $y$, $xy$} and relations: $$ x^{2}=1,\;\;\;\;\; y^{2}=1+x+xy.$$We prove that when the rank of $\mathbb{Z}_{+}$-module $n\geq5$, there does not exist irreducible $\mathbb{Z}_{+}$-modules and when the rank $n\leq4$, there exists finite inequivalent irreducible $\mathbb{Z}_{+}$-modules, the number of which is respectively 1, 3, 3, 2 when the rank runs from 1 to 4. 相似文献
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P. N. Dowling W. B. Johnson C. J. Lennard B. Turett 《Proceedings of the American Mathematical Society》1997,125(1):167-174
A renorming of , explored here in detail, shows that the copies of produced in the proof of the Kadec-Pelczynski theorem inside nonreflexive subspaces of cannot be produced inside general nonreflexive spaces that contain copies of . Put differently, James's distortion theorem producing one-plus-epsilon-isomorphic copies of inside any isomorphic copy of is, in a certain sense, optimal. A similar renorming of shows that James's distortion theorem for is likewise optimal.