{"title":"数字拓扑中的凸性和冻结集","authors":"L. Boxer","doi":"10.4995/AGT.2021.14185","DOIUrl":null,"url":null,"abstract":"We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a \"thick\" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Convexity and freezing sets in digital topology\",\"authors\":\"L. Boxer\",\"doi\":\"10.4995/AGT.2021.14185\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a \\\"thick\\\" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.\",\"PeriodicalId\":8454,\"journal\":{\"name\":\"arXiv: Geometric Topology\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4995/AGT.2021.14185\",\"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: Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4995/AGT.2021.14185","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.
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