基数函数、谱和强惠特尼收敛

IF 0.4 4区数学 Q4 MATHEMATICS

Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2022-02-04 DOI:10.36045/j.bbms.220204

T. Chauhan, V. Jindal

{"title":"基数函数、谱和强惠特尼收敛","authors":"T. Chauhan, V. Jindal","doi":"10.36045/j.bbms.220204","DOIUrl":null,"url":null,"abstract":"Let $C(X)$ be the set of all real valued continuous functions on a metric space $(X,d)$. Caserta introduced the topology of strong Whitney convergence on bornology for $C(X)$ in [A. Caserta, Strong Whitney convergence, Filomat, 2012], which is a generalization of the topology of strong uniform convergence on bornology introduced by Beer-Levi in [Beer-Levi, Strong uniform continuity, J. Math. Anal. Appl., 2009]. The purpose of this paper is to study various cardinal invariants of the function space $C(X)$ endowed with the topologies of strong Whitney and Whitney convergence on bornology. In the process, we present simpler proofs of a number of results from the literature. In the end, relationships between cardinal invariants of strong Whitney convergence and strong uniform convergence on $C(X)$ have also been studied.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Cardinal Functions, Bornologies and Strong Whitney convergence\",\"authors\":\"T. Chauhan, V. Jindal\",\"doi\":\"10.36045/j.bbms.220204\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $C(X)$ be the set of all real valued continuous functions on a metric space $(X,d)$. Caserta introduced the topology of strong Whitney convergence on bornology for $C(X)$ in [A. Caserta, Strong Whitney convergence, Filomat, 2012], which is a generalization of the topology of strong uniform convergence on bornology introduced by Beer-Levi in [Beer-Levi, Strong uniform continuity, J. Math. Anal. Appl., 2009]. The purpose of this paper is to study various cardinal invariants of the function space $C(X)$ endowed with the topologies of strong Whitney and Whitney convergence on bornology. In the process, we present simpler proofs of a number of results from the literature. In the end, relationships between cardinal invariants of strong Whitney convergence and strong uniform convergence on $C(X)$ have also been studied.\",\"PeriodicalId\":55309,\"journal\":{\"name\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-02-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/j.bbms.220204\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Belgian Mathematical Society-Simon Stevin","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/j.bbms.220204","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

设C(X)$是度量空间$(X,d)$上所有实值连续函数的集合。Caserta在[A]中引入了$C(X)$的本体上的强Whitney收敛拓扑。Caserta, Strong Whitney convergence, Filomat, 2012]，这是对Beer-Levi在[Beer-Levi, Strong uniform continuity, J. Math]中引入的bornology上的强一致收敛拓扑的推广。分析的达成。, 2009]。本文的目的是研究具有强惠特尼和惠特尼收敛拓扑的函数空间$C(X)$的各种基数不变量。在此过程中，我们对文献中的一些结果提出了更简单的证明。最后，研究了C(X)$上的强惠特尼收敛与强一致收敛的基数不变量之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Cardinal Functions, Bornologies and Strong Whitney convergence

Let $C(X)$ be the set of all real valued continuous functions on a metric space $(X,d)$. Caserta introduced the topology of strong Whitney convergence on bornology for $C(X)$ in [A. Caserta, Strong Whitney convergence, Filomat, 2012], which is a generalization of the topology of strong uniform convergence on bornology introduced by Beer-Levi in [Beer-Levi, Strong uniform continuity, J. Math. Anal. Appl., 2009]. The purpose of this paper is to study various cardinal invariants of the function space $C(X)$ endowed with the topologies of strong Whitney and Whitney convergence on bornology. In the process, we present simpler proofs of a number of results from the literature. In the end, relationships between cardinal invariants of strong Whitney convergence and strong uniform convergence on $C(X)$ have also been studied.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.