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本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若$X,Y$为$\aleph_0$空间,则$X$到$Y$上的点紧致的连续集值映射族依紧开拓扑是$\aleph_{0}$空间,从而将Michael$^{[1]}$的结论推广到更大的映射空间类上. 相似文献
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利用拓扑博弈G(DC,X)的理论,推广了关于meso-紧空间有限乘积性质并得到如下结果:(1)如果(V)i∈ω,Yi是正则DC-like的meso-紧空间,则∏iωYi是meso-紧的;(2)如果(V)i∈ω,Yi是正则C-散射meso-紧的P-空间,则∏i∈ωYi是meso-紧的. 相似文献
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本文主要建立由分数次积分$I_{\gamma}$与函数$b\in\mathrm{Lip}_{\beta}(\mu)$生成的交换子$[b, I_{\gamma}]$在以满足几何双倍与上部双倍条件的非齐度量测度空间为底空间的Morrey空间上紧性的充要条件.在假设控制函数$\lambda$满足逆双倍条件下,证明了交换子$[b,I_{\gamma}]$为从Morrey空间$M^{p}_{q}(\mu)$到$M^{s}_{t}(\mu)$紧性当且仅当$b\in\mathrm{Lip}_{\beta}(\mu)$. 相似文献
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在这篇文章中, 我们得到了一个偏微分方程,这个方程可以用来描述具有迷向$\textbf{E}$曲率的球对称的芬斯勒度量,通过这个方程,我们讨论了一种特殊的情况. 相似文献
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证明了在逆序列的情形下,可遮空间、强可遮空间在假设X是可数仿紧空间的条件下可被其极限空间保持,进一步证明了遗传可遮,遗传强可遮及遗传σ-亚紧性在无需对投射及极限空间X做任何假设的情况下即可被其逆极限空间保持.作为上述两个结果的应用,分别给出了两个相关的可数Tychonoff乘积定理. 相似文献
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遗传σ-亚紧空间及其乘积性质 总被引:8,自引:0,他引:8
本文首先获得遗传σ 亚紧空间的一组等价刻划.然后,利用这组刻划得到了这类空间的两个Tychonof乘积定理以及关于σ 积的定理.最后指出:本文得到的遗传σ 亚紧空间的两个Tychonof乘积定理在σ 亚紧的情形下不成立. 相似文献
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本文主要研究了$\mathbb{Z}^{k}$-作用一维子系统的跟踪性质. 文中运用两种等价的方式引入了$\mathbb{Z}^{k}$-作用一维子系统的伪轨以及跟踪性的概念. 对于一个闭黎曼流形上的光滑$\mathbb{Z}^{k}$-作用$T$, 我们通过诱导的非自治动力系统提出了Anosov方向的概念. 借助Bowen几何的方法, 我们证明了$T$沿着任意Anosov方向具有Lipschitz跟踪性. 相似文献
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For positive integers j and k with j ≥ k, an L(j, k)-labeling of a graph G is an assignment of nonnegative integers to V(G) such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L(j, k)-labeling of a graph G is the difference between the maximum and minimum integers it uses. The λj, k-number of G is the minimum span taken over all L(j, k)-labelings of G. An m-(j, k)-circular labeling of a graph G is a function f : V(G) →{0, 1, 2,..., m - 1} such that |f(u) - f(v)|m ≥ j if u and v are adjacent; and |f(u) - f(v)|m 〉 k ifu and v are at distance two, where |x|m = min{|xl|, m-|x|}. The minimum integer m such that there exists an m-(j, k)-circular labeling of G is called the σj,k-number of G and is denoted by σj,k(G). This paper determines the σ2,1-number of the Cartesian product of any three complete graphs. 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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{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces 下载免费PDF全文
Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$. 相似文献
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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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Bo Lu 《数学研究通讯:英文版》2013,29(1):41-50
Let $R$ be a ring, and let $(\mathcal{F}, C)$ be a cotorsion theory. In this article, the
notion of $\mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect rings
and A-perfect rings. A ring $R$ is said to be right $\mathcal{F}$-perfect if $F$ is projective relative
to $R$ for any $F ∈ \mathcal{F}$. We give some characterizations of $\mathcal{F}$-perfect rings. For example,
we show that a ring $R$ is right $\mathcal{F}$-perfect if and only if $\mathcal{F}$-covers of finitely generated
modules are projective. Moreover, we define $\mathcal{F}$-perfect modules and investigate some
properties of them. 相似文献
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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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Danny Calegari Nathan M. Dunfield 《Proceedings of the American Mathematical Society》2006,134(11):3131-3136
We give an example of a subgroup of which is a strictly ascending HNN extension of a non-abelian finitely generated free group . In particular, we exhibit a free group in of rank which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir (2005). The main ingredient in our construction is a specific finite volume (non-compact) hyperbolic 3-manifold which is a surface bundle over the circle. In particular, most of comes from the fundamental group of a surface fiber. A key feature of is that there is an element of in with an eigenvalue which is the square root of a rational integer. We also use the Bass-Serre tree of a field with a discrete valuation to show that the group we construct is actually free.
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本文介绍一致空间的理想导集映射,并对这些映射的像展开研究.同时,介绍I-Hurewicz有界性的概念,研究I-Hurewicz有界性的基础拓扑运算性质.最后,得到一致空间中I-Hurewicz有界性的一个等价刻画. 相似文献
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S. Mrowka 《Proceedings of the American Mathematical Society》2000,128(12):3701-3709
Answering a question of Arhangel'skii, we show - under GCH - that for most cardinals there exists an -compact space such that but does not embed in a closed fashion into the product of copies of .
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1977年,刘应明引进拟仿紧性并证明了下述集论拓扑学的结果:在假设$2^{\omega_1}>2^{\omega}$下每一个可分正规的拟仿紧空间是仿紧空间.我们进一步证明假设$2^{\omega_1}>2^{\omega}$等价于每一个可分正规的拟仿紧空间是仿紧空间,获得了拟仿紧性的一个独立性结果. 相似文献