{"title":"条形是唯一断开平面的开放凸集","authors":"R. Mortini, P. Pflug","doi":"10.1080/0025570X.2023.2165855","DOIUrl":null,"url":null,"abstract":"Summary We show that the number of complementary components of an open convex set in the plane is 0, 1, or 2 by showing that isometric images of strips (where I is a bounded open interval) are the only open convex sets in with disconnected complement.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Strips Are the Only Open Convex Sets that Disconnect the Plane\",\"authors\":\"R. Mortini, P. Pflug\",\"doi\":\"10.1080/0025570X.2023.2165855\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary We show that the number of complementary components of an open convex set in the plane is 0, 1, or 2 by showing that isometric images of strips (where I is a bounded open interval) are the only open convex sets in with disconnected complement.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2023.2165855\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570X.2023.2165855","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Strips Are the Only Open Convex Sets that Disconnect the Plane
Summary We show that the number of complementary components of an open convex set in the plane is 0, 1, or 2 by showing that isometric images of strips (where I is a bounded open interval) are the only open convex sets in with disconnected complement.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
