{"title":"缓慢振荡函数的网格","authors":"Yutaka Iwamoto","doi":"arxiv-2405.19555","DOIUrl":null,"url":null,"abstract":"We show that lattice isomorphisms between the lattices of slowly oscillating\nfunctions on chain-connected proper metric spaces induce coarsely equivalent\nhomeomorphisms. This result leads to a Banach-Stone-type theorem for these\nlattices. Furthermore, we provide a representation theorem that characterizes\nlinear lattice isomorphisms among these lattices.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"87 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lattices of slowly oscillating functions\",\"authors\":\"Yutaka Iwamoto\",\"doi\":\"arxiv-2405.19555\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that lattice isomorphisms between the lattices of slowly oscillating\\nfunctions on chain-connected proper metric spaces induce coarsely equivalent\\nhomeomorphisms. This result leads to a Banach-Stone-type theorem for these\\nlattices. Furthermore, we provide a representation theorem that characterizes\\nlinear lattice isomorphisms among these lattices.\",\"PeriodicalId\":501314,\"journal\":{\"name\":\"arXiv - MATH - General Topology\",\"volume\":\"87 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - General Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2405.19555\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.19555","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that lattice isomorphisms between the lattices of slowly oscillating
functions on chain-connected proper metric spaces induce coarsely equivalent
homeomorphisms. This result leads to a Banach-Stone-type theorem for these
lattices. Furthermore, we provide a representation theorem that characterizes
linear lattice isomorphisms among these lattices.
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