{"title":"有序群o-极小展开中可定义的Tietze扩张性质","authors":"Masato Fujita","doi":"10.1007/s00153-023-00875-5","DOIUrl":null,"url":null,"abstract":"<div><p>The following two assertions are equivalent for an o-minimal expansion of an ordered group <span>\\(\\mathcal M=(M,<,+,0,\\ldots )\\)</span>. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function <span>\\(f:A \\rightarrow M\\)</span> defined on a definable closed subset of <span>\\(M^n\\)</span> has a definable continuous extension <span>\\(F:M^n \\rightarrow M\\)</span>.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Definable Tietze extension property in o-minimal expansions of ordered groups\",\"authors\":\"Masato Fujita\",\"doi\":\"10.1007/s00153-023-00875-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The following two assertions are equivalent for an o-minimal expansion of an ordered group <span>\\\\(\\\\mathcal M=(M,<,+,0,\\\\ldots )\\\\)</span>. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function <span>\\\\(f:A \\\\rightarrow M\\\\)</span> defined on a definable closed subset of <span>\\\\(M^n\\\\)</span> has a definable continuous extension <span>\\\\(F:M^n \\\\rightarrow M\\\\)</span>.</p></div>\",\"PeriodicalId\":48853,\"journal\":{\"name\":\"Archive for Mathematical Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00153-023-00875-5\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-023-00875-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
Definable Tietze extension property in o-minimal expansions of ordered groups
The following two assertions are equivalent for an o-minimal expansion of an ordered group \(\mathcal M=(M,<,+,0,\ldots )\). There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function \(f:A \rightarrow M\) defined on a definable closed subset of \(M^n\) has a definable continuous extension \(F:M^n \rightarrow M\).
期刊介绍：
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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