{"title":"由任意自然数生成的对象。第4部分:新方面","authors":"Krassimir Atanassov","doi":"10.7546/nntdm.2023.29.3.589-597","DOIUrl":null,"url":null,"abstract":"The set $\\underline{SET}(n)$, generated by an arbitrary natural number $n$, was defined in [3]. There, and in [5,6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of $\\underline{SET}(n)$. Here, over the elements of $\\underline{SET}(n)$ new arithmetic functions are defined and some of their basic properties are studied. Two standard modal topological structures over $\\underline{SET}(n)$ are described. Perspectives for future research are discussed.","PeriodicalId":44060,"journal":{"name":"Notes on Number Theory and Discrete Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Objects generated by an arbitrary natural number. Part 4: New aspects\",\"authors\":\"Krassimir Atanassov\",\"doi\":\"10.7546/nntdm.2023.29.3.589-597\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The set $\\\\underline{SET}(n)$, generated by an arbitrary natural number $n$, was defined in [3]. There, and in [5,6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of $\\\\underline{SET}(n)$. Here, over the elements of $\\\\underline{SET}(n)$ new arithmetic functions are defined and some of their basic properties are studied. Two standard modal topological structures over $\\\\underline{SET}(n)$ are described. Perspectives for future research are discussed.\",\"PeriodicalId\":44060,\"journal\":{\"name\":\"Notes on Number Theory and Discrete Mathematics\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notes on Number Theory and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/nntdm.2023.29.3.589-597\",\"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":"Notes on Number Theory and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/nntdm.2023.29.3.589-597","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Objects generated by an arbitrary natural number. Part 4: New aspects
The set $\underline{SET}(n)$, generated by an arbitrary natural number $n$, was defined in [3]. There, and in [5,6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of $\underline{SET}(n)$. Here, over the elements of $\underline{SET}(n)$ new arithmetic functions are defined and some of their basic properties are studied. Two standard modal topological structures over $\underline{SET}(n)$ are described. Perspectives for future research are discussed.
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