度量空间的拓扑方面

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-04-11 DOI:10.1007/s10711-024-00921-3

Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya

{"title":"度量空间的拓扑方面","authors":"Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya","doi":"10.1007/s10711-024-00921-3","DOIUrl":null,"url":null,"abstract":"<p>Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"6 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological aspects of the space of metric measure spaces\",\"authors\":\"Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya\",\"doi\":\"10.1007/s10711-024-00921-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.</p>\",\"PeriodicalId\":55103,\"journal\":{\"name\":\"Geometriae Dedicata\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometriae Dedicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10711-024-00921-3\",\"RegionNum\":4,\"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":"Geometriae Dedicata","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10711-024-00921-3","RegionNum":4,"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

格罗莫夫在公度量空间的同构类空间上引入了两个距离函数，即箱距离和可观测距离，并发展了公度量空间的收敛理论。为了深入理解收敛理论，我们研究了配备这些距离函数的空间上的几个拓扑性质。

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

Topological aspects of the space of metric measure spaces

Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.

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

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.