Pub Date : 2023-11-13DOI: 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.
{"title":"Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space","authors":"Weiller F. C. Barboza, Henrique F. de Lima, Marco A. L. Velásquez","doi":"10.14712/1213-7243.2023.013","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.013","url":null,"abstract":"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.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"39 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 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。
{"title":"Universality, complexity and asymptotically uniformly smooth Banach spaces","authors":"R Causey, Gilles Lancien","doi":"10.14712/1213-7243.2023.015","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.015","url":null,"abstract":"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 $p=infty$.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"8 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 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.
{"title":"A countably cellular topological group all of whose countable subsets are closed need not be $mathbb{R}$-factorizable","authors":"Mikhail Tkachenko","doi":"10.14712/1213-7243.2023.016","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.016","url":null,"abstract":"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.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"32 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 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。
{"title":"A note on functional tightness and minitightness of space of the $G$-permutation degree","authors":"Dimitrios N. Georgiou, Nodirbek K. Mamadaliev, Rustam M. Zhuraev","doi":"10.14712/1213-7243.2023.019","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.019","url":null,"abstract":"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.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"88 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136346959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 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.
{"title":"Special sets of reals and weak forms of normality on Isbell--Mrówka spaces","authors":"Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki","doi":"10.14712/1213-7243.2023.014","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.014","url":null,"abstract":"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.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"39 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.14712/1213-7243.2023.005
Jing Lu, Bin Zhao, K. Wang, Dongsheng Zhao
{"title":"Quasicontinuous spaces","authors":"Jing Lu, Bin Zhao, K. Wang, Dongsheng Zhao","doi":"10.14712/1213-7243.2023.005","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.005","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42850427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.14712/1213-7243.2023.004
Barry James Gardner
{"title":"Mal'tsev--Neumann products of semi-simple classes of rings","authors":"Barry James Gardner","doi":"10.14712/1213-7243.2023.004","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.004","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41617559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.14712/1213-7243.2023.006
Reza Jafarpour-Golzari
{"title":"Degree polynomial for vertices in a graph and its behavior under graph operations","authors":"Reza Jafarpour-Golzari","doi":"10.14712/1213-7243.2023.006","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.006","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45793125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-28DOI: 10.14712/1213-7243.2023.007
Luděk Zajíček
{"title":"On sets of discontinuities of functions continuous on all lines","authors":"Luděk Zajíček","doi":"10.14712/1213-7243.2023.007","DOIUrl":"https://doi.org/10.14712/1213-7243.2023.007","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47010581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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