{"title":"格序群上的拓扑","authors":"H. Wu, Qingguo Li, Bin Yu","doi":"10.22436/JNSA.011.05.10","DOIUrl":null,"url":null,"abstract":"We introduce the concept of the strong-positive cone in a lattice-ordered group (G,6, ·) and define the continuous latticeordered group. We also investigate the C-topology and bi-C-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) (G,6, ·) is a continuous lattice-ordered group if and only if (G,6) is a continuous poset; (2) for the bi-C-topology τ in a continuous lattice-ordered group (G,6, ·), (G, ·, τ) is a topological group and (G,6, τ) is a topological lattice.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"9 1","pages":"701-712"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A topology on lattice-ordered groups\",\"authors\":\"H. Wu, Qingguo Li, Bin Yu\",\"doi\":\"10.22436/JNSA.011.05.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the concept of the strong-positive cone in a lattice-ordered group (G,6, ·) and define the continuous latticeordered group. We also investigate the C-topology and bi-C-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) (G,6, ·) is a continuous lattice-ordered group if and only if (G,6) is a continuous poset; (2) for the bi-C-topology τ in a continuous lattice-ordered group (G,6, ·), (G, ·, τ) is a topological group and (G,6, τ) is a topological lattice.\",\"PeriodicalId\":22770,\"journal\":{\"name\":\"The Journal of Nonlinear Sciences and Applications\",\"volume\":\"9 1\",\"pages\":\"701-712\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Nonlinear Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/JNSA.011.05.10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.011.05.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce the concept of the strong-positive cone in a lattice-ordered group (G,6, ·) and define the continuous latticeordered group. We also investigate the C-topology and bi-C-topology given on a lattice-ordered group. The main results obtained in this paper are as follows: (1) (G,6, ·) is a continuous lattice-ordered group if and only if (G,6) is a continuous poset; (2) for the bi-C-topology τ in a continuous lattice-ordered group (G,6, ·), (G, ·, τ) is a topological group and (G,6, τ) is a topological lattice.
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