{"title":"持久性图集合上的强拓扑","authors":"V. Kiosak, A. Savchenko, M. Zarichnyi","doi":"10.1063/1.5130798","DOIUrl":null,"url":null,"abstract":"We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described. \nAlso, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"65 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":"{\"title\":\"Strong topology on the set of persistence diagrams\",\"authors\":\"V. Kiosak, A. Savchenko, M. Zarichnyi\",\"doi\":\"10.1063/1.5130798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described. \\nAlso, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.\",\"PeriodicalId\":179088,\"journal\":{\"name\":\"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19\",\"volume\":\"65 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"21\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/1.5130798\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.5130798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Strong topology on the set of persistence diagrams
We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described.
Also, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.
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