关于Effros定理的范围

IF 0.5 3区数学 Q3 MATHEMATICS

Fundamenta Mathematicae Pub Date : 2021-07-24 DOI:10.4064/fm100-12-2021

Andrea Medini

{"title":"关于Effros定理的范围","authors":"Andrea Medini","doi":"10.4064/fm100-12-2021","DOIUrl":null,"url":null,"abstract":"All spaces (and groups) are assumed to be separable and metrizable. Jan van Mill showed that every analytic group G is Effros (that is, every continuous transitive action of G on a non-meager space is micro-transitive). We complete the picture by obtaining the following results: • Under AC, there exists a non-Effros group, • Under AD, every group is Effros, • Under V = L, there exists a coanalytic non-Effros group. The above counterexamples will be graphs of discontinuous homomorphisms.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the scope of the Effros theorem\",\"authors\":\"Andrea Medini\",\"doi\":\"10.4064/fm100-12-2021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"All spaces (and groups) are assumed to be separable and metrizable. Jan van Mill showed that every analytic group G is Effros (that is, every continuous transitive action of G on a non-meager space is micro-transitive). We complete the picture by obtaining the following results: • Under AC, there exists a non-Effros group, • Under AD, every group is Effros, • Under V = L, there exists a coanalytic non-Effros group. The above counterexamples will be graphs of discontinuous homomorphisms.\",\"PeriodicalId\":55138,\"journal\":{\"name\":\"Fundamenta Mathematicae\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamenta Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/fm100-12-2021\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/fm100-12-2021","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

假设所有的空间（和组）都是可分离的和可度量的。Jan van Mill证明了每一个分析群G都是Effros（即G在非穷空间上的每一个连续传递作用都是微传递的）。我们通过获得以下结果来完成这幅图：•在AC下，存在一个非Effros组，•在AD下，每个组都是Effros，•在V=L下，存在着一个共分析非Effos组。上面的反例将是不连续同态的图。

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

On the scope of the Effros theorem

All spaces (and groups) are assumed to be separable and metrizable. Jan van Mill showed that every analytic group G is Effros (that is, every continuous transitive action of G on a non-meager space is micro-transitive). We complete the picture by obtaining the following results: • Under AC, there exists a non-Effros group, • Under AD, every group is Effros, • Under V = L, there exists a coanalytic non-Effros group. The above counterexamples will be graphs of discontinuous homomorphisms.

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

Fundamenta Mathematicae 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： FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.