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Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space 重温沉浸在局部对称半黎曼空间中的线性Weingarten类空间子流形
Q4 MATHEMATICS Pub Date : 2023-11-13 DOI: 10.14712/1213-7243.2023.013
Weiller F. C.  Barboza, Henrique F. de Lima, Marco A. L. Velásquez
In this paper, we deal with $n$-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space $L_{p}^{n+p}$ of index $p>1$, which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric submanifold of the ambient space. For this, we use three main core analytical tools: a suitable version of the Omori--Yau maximum principle, parabolicity with respect to a modified Cheng--Yau operator and a certain integrability property.
本文研究了指标p>1$的局部对称半黎曼空间$L_{p}^{n+p}$中浸入平行归一化平均曲率向量场和平面法向束的$n$维完全线性Weingarten类空间子流形,该空间服从某些曲率约束(这种环境空间可视为半黎曼空间形式的扩展)。在适当的假设下,我们能够证明这种类空间子流形与环境空间的等参子流形是完全脐形或等距形的。为此,我们使用了三个主要的核心分析工具:适当版本的Omori—Yau极大原理,关于改进Cheng—Yau算子的抛物性和一定的可积性。
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引用次数: 0
Universality, complexity and asymptotically uniformly smooth Banach spaces 通用性、复杂性与渐近一致光滑Banach空间
Q4 MATHEMATICS Pub Date : 2023-11-13 DOI: 10.14712/1213-7243.2023.015
R Causey, Gilles Lancien
For $1 < p le infty$, we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent $p$-asymptotically uniformly smooth norm. We prove that this class is analytic complete in the class of separable Banach spaces. These results extend previous works by N. J. Kalton, D. Werner and O. Kurka in the case $p=infty$.
对于$1 < p le infty$,我们证明了具有等价的$p$ -渐近一致光滑范数的所有可分Banach空间类的单射和满射泛的Banach空间的存在性。在可分离巴拿赫空间中证明了该类是解析完备的。这些结果扩展了N. J. Kalton, D. Werner和O. Kurka在$p=infty$案例中的先前工作。
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引用次数: 1
A countably cellular topological group all of whose countable subsets are closed need not be $mathbb{R}$-factorizable 一个可数元胞拓扑群,其所有可数子集都是闭的,不必是$mathbb{R}$-可因数的
Q4 MATHEMATICS Pub Date : 2023-11-13 DOI: 10.14712/1213-7243.2023.016
Mikhail  Tkachenko
We construct a Hausdorff topological group $G$ such that $aleph_1$ is a precalibre of $G$ (hence, $G$ has countable cellularity), all countable subsets of $G$ are closed and $C$-embedded in $G$, but $G$ is not $mathbb{R}$-factorizable. This solves Problem 8.6.3 from the book ``Topological Groups and Related Structures" (2008) in the negative.
构造了一个Hausdorff拓扑群$G$,使得$G$是$G$的不定数(因此,$G$具有可数胞性),$G$的所有可数子集都是闭的,$C$-嵌入在$G$中,但$G$不是$mathbb{R}$-可因数的。这就从反面解决了《拓扑群与相关结构》(2008)一书中的8.6.3题。
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引用次数: 0
A note on functional tightness and minitightness of space of the $G$-permutation degree 关于$G$-置换度空间的功能密性和微密性的一个注记
Q4 MATHEMATICS Pub Date : 2023-11-13 DOI: 10.14712/1213-7243.2023.019
Dimitrios N.  Georgiou, Nodirbek K. Mamadaliev, Rustam M. Zhuraev
We study the behavior of the minimal tightness and functional tightness of topological spaces under the influence of the functor of the permutation degree. Analytically: a) We introduce the notion of $tau$-open sets and investigate some basic properties of them. b) We prove that if the map $fcolon Xrightarrow Y$ is $tau$-continuous, then the map $SP^{n}fcolon SP^n X rightarrow SP^n Y$ is also $tau$-continuous. c) We show that the functor $SP^n$ preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on $tau$-bounded spaces. More precisely, we prove that the functor of permutation degree $SP^n$ preserves the property of being $tau$-bounded.
研究了拓扑空间在置换度函子影响下的最小紧度和泛函紧度的行为。解析:a)引入$tau$ -开集的概念,研究了它们的一些基本性质。b)我们证明了如果映射$fcolon Xrightarrow Y$是$tau$连续的,那么映射$SP^{n}fcolon SP^n X rightarrow SP^n Y$也是$tau$连续的。c)证明函子$SP^n$保留了紧的函数紧密性和最小紧密性。d)最后给出了$tau$ -有界空间的一些事实和性质。更确切地说,我们证明了置换度$SP^n$的函子保持了$tau$有界的性质。
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引用次数: 0
Special sets of reals and weak forms of normality on Isbell--Mrówka spaces Isbell- Mrówka空间上的实数和弱正规形式的特殊集合
Q4 MATHEMATICS Pub Date : 2023-11-13 DOI: 10.14712/1213-7243.2023.014
Vinicius  de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki
We recall some classical results relating normality and some natural weakenings of normality in $Psi$-spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$-sets, $lambda$-sets and $sigma$-sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being $aleph_0$-separated. This new class fits between $lambda$-sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $mathcal A$ being potentially almost-normal (pseudonormal), in the sense that $mathcal A$ is almost-normal (pseudonormal) in some c.c.c. forcing extension.
我们回顾了一些经典的结果,将Cantor树几乎不相交的分支族上的$Psi$ -空间中的正态性和正态性的一些自然弱性与诸如$Q$ -sets, $lambda$ -sets和$sigma$ -sets等实数的特殊集合联系起来。我们引入了一类新的特殊实数集,它们对应于相应的几乎不相交的$aleph_0$ -分离分支族。这个新类介于$lambda$ -set和完全贫乏的set之间。我们还讨论了一个几乎不相交的族$mathcal A$是潜在的几乎正态(伪正态)的条件,在某种意义上$mathcal A$在某些cc强迫扩展中是几乎正态(伪正态)的。
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引用次数: 0
Quasicontinuous spaces Quasicontinuous空间
IF 0.2 Q4 MATHEMATICS Pub Date : 2023-04-28 DOI: 10.14712/1213-7243.2023.005
Jing  Lu, Bin Zhao, K. Wang, Dongsheng Zhao
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引用次数: 0
Mal'tsev--Neumann products of semi-simple classes of rings Mal’tsev——半简单环类的Neumann乘积
IF 0.2 Q4 MATHEMATICS Pub Date : 2023-04-28 DOI: 10.14712/1213-7243.2023.004
Barry James  Gardner
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引用次数: 0
Degree polynomial for vertices in a graph and its behavior under graph operations 图中顶点的次多项式及其在图操作下的行为
IF 0.2 Q4 MATHEMATICS Pub Date : 2023-04-28 DOI: 10.14712/1213-7243.2023.006
Reza  Jafarpour-Golzari
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引用次数: 0
On sets of discontinuities of functions continuous on all lines 在所有直线上连续的函数的不连续集合上
IF 0.2 Q4 MATHEMATICS Pub Date : 2023-04-28 DOI: 10.14712/1213-7243.2023.007
Luděk  Zajíček
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引用次数: 0
Some isomorphic properties in projective tensor products 投影张量积中的一些同构性质
IF 0.2 Q4 MATHEMATICS Pub Date : 2023-04-28 DOI: 10.14712/1213-7243.2023.008
Ioana  Ghenciu
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引用次数: 0
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