arXiv - MATH - General Topology最新文献_第9页

Point-set games and functions with the hereditary small oscillation property 具有遗传小振荡特性的点集博弈和函数

arXiv - MATH - General Topology Pub Date : 2024-05-24 DOI: arxiv-2405.15263

Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca

引用次数: 0

New directions in fixed point theory in $G$-metric spaces and applications to mappings contracting perimeters of triangles G$计量空间定点理论的新方向及在三角形周长收缩映射中的应用

arXiv - MATH - General Topology Pub Date : 2024-05-19 DOI: arxiv-2405.11648

Mohamed Jleli, Cristina Maria Pacurar, Bessem Samet

{"title":"New directions in fixed point theory in $G$-metric spaces and applications to mappings contracting perimeters of triangles","authors":"Mohamed Jleli, Cristina Maria Pacurar, Bessem Samet","doi":"arxiv-2405.11648","DOIUrl":"https://doi.org/arxiv-2405.11648","url":null,"abstract":"We are concerned with the study of fixed points for mappings $T: Xto X$,\u0000where $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the\u0000publication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006)\u0000289--297] by Mustafa and Sims, a great interest was devoted to the study of\u0000fixed points in $G$-metric spaces. In 2012, the first and third authors\u0000observed that several fixed point theorems established in $G$-metric spaces are\u0000immediate consequences of known fixed point theorems in standard metric spaces.\u0000This observation demotivated the investigation of fixed points in $G$-metric\u0000spaces. In this paper, we open new directions in fixed point theory in\u0000$G$-metric spaces. Namely, we establish new versions of the Banach, Kannan and\u0000Reich fixed point theorems in $G$-metric spaces. We point out that the approach\u0000used by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1--7]\u0000is inapplicable in the present study. We also provide some interesting\u0000applications related to mappings contracting perimeters of triangles.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153204","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}

引用次数: 0

Continuous operators from spaces of Lipschitz functions 来自 Lipschitz 函数空间的连续算子

arXiv - MATH - General Topology Pub Date : 2024-05-16 DOI: arxiv-2405.09930

Christian Bargetz, Jerzy Kąkol, Damian Sobota

{"title":"Continuous operators from spaces of Lipschitz functions","authors":"Christian Bargetz, Jerzy Kąkol, Damian Sobota","doi":"arxiv-2405.09930","DOIUrl":"https://doi.org/arxiv-2405.09930","url":null,"abstract":"We study the existence of continuous (linear) operators from the Banach\u0000spaces $mathrm{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$\u0000vanishing at a distinguished point and from their predual spaces\u0000$mathcal{F}(M)$ onto certain Banach spaces, including $C(K)$-spaces and the\u0000spaces $c_0$ and $ell_1$. For pairs of spaces $mathrm{Lip}_0(M)$ and $C(K)$\u0000we prove that if they are endowed with topologies weaker than the norm\u0000topology, then usually no continuous (linear or not) surjection exists between\u0000those spaces. We show that, given a Banach space $E$, there exists a continuous\u0000operator from a Lipschitz-free space $mathcal{F}(M)$ onto $E$ if and only if\u0000$mathcal{F}(M)$ contains a subset homeomorphic to $E$ if and only if $d(M)ge\u0000d(E)$. We obtain a new characterization of the Schur property for spaces\u0000$mathcal{F}(M)$: a space $mathcal{F}(M)$ has the Schur property if and only\u0000if for every discrete metric space $N$ with cardinality $d(M)$ the spaces\u0000$mathcal{F}(M)$ and $mathcal{F}(N)$ are weakly sequentially homeomorphic. It\u0000is also showed that if a metric space $M$ contains a bilipschitz copy of the\u0000unit sphere $S_{c_0}$ of the space $c_0$, then $mathrm{Lip}_0(M)$ admits a\u0000continuous operator onto $ell_1$ and hence onto $c_0$. We provide several\u0000conditions for a space $M$ implying that $mathrm{Lip}_0(M)$ is not a\u0000Grothendieck space.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060500","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}

引用次数: 0

Strong Forms of Weakly e-continuous Functions 弱 e-continuous 函数的强形式

arXiv - MATH - General Topology Pub Date : 2024-05-15 DOI: arxiv-2405.09294

B. S. Ayhan

引用次数: 0

$Γ(X)$ as Polish Space $Γ(X)$为波兰空间

arXiv - MATH - General Topology Pub Date : 2024-05-15 DOI: arxiv-2405.09437

Edwar Alexis Ramírez Ardila

引用次数: 0

Set Convergences via bornology 通过 "出生学 "进行集合会聚

arXiv - MATH - General Topology Pub Date : 2024-05-13 DOI: arxiv-2405.07705

Yogesh Agarwal, Varun Jindal

{"title":"Set Convergences via bornology","authors":"Yogesh Agarwal, Varun Jindal","doi":"arxiv-2405.07705","DOIUrl":"https://doi.org/arxiv-2405.07705","url":null,"abstract":"This paper examines the equivalence between various set convergences, as\u0000studied in [7, 13, 22], induced by an arbitrary bornology $mathcal{S}$ on a\u0000metric space $(X,d)$. Specifically, it focuses on the upper parts of the\u0000following set convergences: convergence deduced through uniform convergence of\u0000distance functionals on $mathcal{S}$ ($tau_{mathcal{S},d}$-convergence);\u0000convergence with respect to gap functionals determined by $mathcal{S}$\u0000($G_{mathcal{S},d}$-convergence); and bornological convergence\u0000($mathcal{S}$-convergence). In particular, we give necessary and sufficient\u0000conditions on the structure of the bornology $mathcal{S}$ for the coincidence\u0000of $tau_{mathcal{S},d}^+$-convergence with\u0000$mathsf{G}_{mathcal{S},d}^+$-convergence, as well as\u0000$tau_{mathcal{S},d}^+$-convergence with $mathcal{S}^+$-convergence. A\u0000characterization for the equivalence of $tau_{mathcal{S},d}^+$-convergence\u0000and $mathcal{S}^+$-convergence, in terms of certain convergence of nets, has\u0000also been given earlier by Beer, Naimpally, and Rodriguez-Lopez in [13]. To\u0000facilitate our study, we first devise new characterizations for\u0000$tau_{mathcal{S},d}^+$-convergence and $mathcal{S}^+$-convergence, which we\u0000call their miss-type characterizations.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929132","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}

引用次数: 0

Fixed Node Determination and Analysis in Directed Acyclic Graphs of Structured Networks 结构化网络有向无环图中固定节点的确定与分析

arXiv - MATH - General Topology Pub Date : 2024-05-10 DOI: arxiv-2405.06236

Nam-jin Park, Yeong-Ung Kim, Hyo-Sung Ahn

引用次数: 0

Composition Rules for Strong Structural Controllability and Minimum Input Problem in Diffusively-Coupled Networks 扩散耦合网络中强结构可控性和最小输入问题的组合规则

arXiv - MATH - General Topology Pub Date : 2024-05-09 DOI: arxiv-2405.05557

Nam-Jin Park, Seong-Ho Kwon, Yoo-Bin Bae, Byeong-Yeon Kim, Kevin L. Moore, Hyo-Sung Ahn

{"title":"Composition Rules for Strong Structural Controllability and Minimum Input Problem in Diffusively-Coupled Networks","authors":"Nam-Jin Park, Seong-Ho Kwon, Yoo-Bin Bae, Byeong-Yeon Kim, Kevin L. Moore, Hyo-Sung Ahn","doi":"arxiv-2405.05557","DOIUrl":"https://doi.org/arxiv-2405.05557","url":null,"abstract":"This paper presents new results and reinterpretation of existing conditions\u0000for strong structural controllability in a structured network determined by the\u0000zero/non-zero patterns of edges. For diffusively-coupled networks with\u0000self-loops, we first establish a necessary and sufficient condition for strong\u0000structural controllability, based on the concepts of dedicated and sharing\u0000nodes. Subsequently, we define several conditions for strong structural\u0000controllability across various graph types by decomposing them into disjoint\u0000path graphs. We further extend our findings by introducing a composition rule,\u0000facilitating the analysis of strong structural controllability in larger\u0000networks. This rule allows us to determine the strong structural\u0000controllability of connected graphs called pactus graphs (a generalization of\u0000the well-known cactus graph) by consideration of the strong structural\u0000controllability of its disjoint component graphs. In this process, we introduce\u0000the notion of a component input node, which is a state node that functions\u0000identically to an external input node. Based on this concept, we present an\u0000algorithm with approximate polynomial complexity to determine the minimum\u0000number of external input nodes required to maintain strong structural\u0000controllability in a diffusively-coupled network with self-loops.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929455","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}

引用次数: 0

Graphs with tranches: consequences for topology and dynamics 有分段的图形：拓扑学和动力学的后果

arXiv - MATH - General Topology Pub Date : 2024-05-08 DOI: arxiv-2405.05407

Michał Kowalewski, Piotr Oprocha

引用次数: 0

A fixed point results of Kannan-type for multi-valued mapping on fuzzy metric spaces 模糊度量空间上多值映射的 Kannan 型定点结果

arXiv - MATH - General Topology Pub Date : 2024-05-07 DOI: arxiv-2405.04179

Shunya Hashimoto, Aqib Saghir

引用次数: 0