{"title":"$\\mathbb{R}^2$上的河度量的一些度量和拓扑性质","authors":"N. Okičić, A. Rekic-Vukovic","doi":"10.37418/amsj.12.2.8","DOIUrl":null,"url":null,"abstract":"In this paper we consider some metrical and topological properties of the river metric $d^*$ in the plane $\\mathbb{R}^2^2$. We give the form of the metric segment and the set of all points that are equidistant from two points in $(\\rR^2,d^*)$. We also give the characterization of a compact sets in this space.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SOME METRICAL AND TOPOLOGICAL PROPERTIES OF THE RIVER METRIC ON $\\\\mathbb{R}^2$\",\"authors\":\"N. Okičić, A. Rekic-Vukovic\",\"doi\":\"10.37418/amsj.12.2.8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider some metrical and topological properties of the river metric $d^*$ in the plane $\\\\mathbb{R}^2^2$. We give the form of the metric segment and the set of all points that are equidistant from two points in $(\\\\rR^2,d^*)$. We also give the characterization of a compact sets in this space.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.12.2.8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.2.8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SOME METRICAL AND TOPOLOGICAL PROPERTIES OF THE RIVER METRIC ON $\mathbb{R}^2$
In this paper we consider some metrical and topological properties of the river metric $d^*$ in the plane $\mathbb{R}^2^2$. We give the form of the metric segment and the set of all points that are equidistant from two points in $(\rR^2,d^*)$. We also give the characterization of a compact sets in this space.
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