{"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}
引用次数: 0
Abstract
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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