非奇异变换群上的拓扑

IF 0.3 Q4 LOGIC Journal of Logic and Analysis Pub Date : 2022-01-01 DOI:10.4115/jla.2022.14.4
François LE MAÎTRE
{"title":"非奇异变换群上的拓扑","authors":"François LE MAÎTRE","doi":"10.4115/jla.2022.14.4","DOIUrl":null,"url":null,"abstract":"In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformations of the real line whose support has finite measure carries no Polish group topology. We then characterize the Borel $\\sigma$-finite measures $\\lambda$ on a standard Borel space for which the group of $\\lambda$-preserving transformations has the automatic continuity property. We finally show that the natural Polish topology on the group of all non-singular transformations is actually its only Polish group topology.","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Polish topologies on groups of non-singular transformations\",\"authors\":\"François LE MAÎTRE\",\"doi\":\"10.4115/jla.2022.14.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformations of the real line whose support has finite measure carries no Polish group topology. We then characterize the Borel $\\\\sigma$-finite measures $\\\\lambda$ on a standard Borel space for which the group of $\\\\lambda$-preserving transformations has the automatic continuity property. We finally show that the natural Polish topology on the group of all non-singular transformations is actually its only Polish group topology.\",\"PeriodicalId\":53872,\"journal\":{\"name\":\"Journal of Logic and Analysis\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic and Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4115/jla.2022.14.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic and Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4115/jla.2022.14.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0

摘要

本文证明了关于非奇异变换群上的波兰群拓扑的几个结果。首先证明了具有有限测度支持的实直线的保测度变换群不携带波兰群拓扑。然后我们在一个标准Borel空间上刻画了Borel $\sigma$ -有限测度$\lambda$,对于该空间,$\lambda$ -保持变换群具有自动连续性。我们最后证明了所有非奇异变换群上的自然波兰拓扑实际上是它唯一的波兰群拓扑。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Polish topologies on groups of non-singular transformations
In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformations of the real line whose support has finite measure carries no Polish group topology. We then characterize the Borel $\sigma$-finite measures $\lambda$ on a standard Borel space for which the group of $\lambda$-preserving transformations has the automatic continuity property. We finally show that the natural Polish topology on the group of all non-singular transformations is actually its only Polish group topology.
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
CiteScore
0.80
自引率
0.00%
发文量
2
审稿时长
35 weeks
期刊介绍: "Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.
期刊最新文献
Fractals and the monadic second order theory of one successor A computational study of a class of recursive inequalities Generalized effective completeness for continuous logic Polish topologies on groups of non-singular transformations Compactness of $\omega^\lambda$ for $\lambda$ singular
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1