Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka
{"title":"Can one recognize a function from its graph?","authors":"Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka","doi":"10.4171/zaa/1730","DOIUrl":null,"url":null,"abstract":"\\We analyse the “interplay” between analytical properties of a real function on a metric space, on the one hand, and topological properties of its graph, on the other. In particular, we study functions with closed, compact, connected, pathwise connected, or locally connected graphs, and we give nine conditions on the graph which are equivalent to the continuity of a function. A main emphasis is put on examples and counterexamples which illustrate how significant our hypotheses are, and how far sufficient conditions are from being necessary.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"54 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift fur Analysis und ihre Anwendungen","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/zaa/1730","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
\We analyse the “interplay” between analytical properties of a real function on a metric space, on the one hand, and topological properties of its graph, on the other. In particular, we study functions with closed, compact, connected, pathwise connected, or locally connected graphs, and we give nine conditions on the graph which are equivalent to the continuity of a function. A main emphasis is put on examples and counterexamples which illustrate how significant our hypotheses are, and how far sufficient conditions are from being necessary.
期刊介绍：
The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications.
To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
