{"title":"正整数集合上公除法拓扑中等差数列的闭包","authors":"P. Szczuka","doi":"10.2478/s11533-013-0394-6","DOIUrl":null,"url":null,"abstract":"In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"31 1","pages":"1008-1014"},"PeriodicalIF":0.0000,"publicationDate":"2014-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The closures of arithmetic progressions in the common division topology on the set of positive integers\",\"authors\":\"P. Szczuka\",\"doi\":\"10.2478/s11533-013-0394-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.\",\"PeriodicalId\":50988,\"journal\":{\"name\":\"Central European Journal of Mathematics\",\"volume\":\"31 1\",\"pages\":\"1008-1014\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Central European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/s11533-013-0394-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-013-0394-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The closures of arithmetic progressions in the common division topology on the set of positive integers
In this paper we characterize the closures of arithmetic progressions in the topology T on the set of positive integers with the base consisting of arithmetic progressions {an + b} such that if the prime number p is a factor of a, then it is also a factor of b. The topology T is called the common division topology.