{"title":"数字图像中的m-$同位距离","authors":"Melih İs, İsmet Karaca","doi":"arxiv-2408.15596","DOIUrl":null,"url":null,"abstract":"We define digital $m-$homotopic distance and its higher version. We also\nmention related notions such as $m-$category in the sense of\nLusternik-Schnirelmann and $m-$complexity in topological robotics. Later, we\nexamine the homotopy invariance or $m-$homotopy invariance property of these\nconcepts.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$m-$homotopic Distances in Digital Images\",\"authors\":\"Melih İs, İsmet Karaca\",\"doi\":\"arxiv-2408.15596\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define digital $m-$homotopic distance and its higher version. We also\\nmention related notions such as $m-$category in the sense of\\nLusternik-Schnirelmann and $m-$complexity in topological robotics. Later, we\\nexamine the homotopy invariance or $m-$homotopy invariance property of these\\nconcepts.\",\"PeriodicalId\":501119,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Topology\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.15596\",\"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 - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15596","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We define digital $m-$homotopic distance and its higher version. We also
mention related notions such as $m-$category in the sense of
Lusternik-Schnirelmann and $m-$complexity in topological robotics. Later, we
examine the homotopy invariance or $m-$homotopy invariance property of these
concepts.
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