| 循环群偏序集上的拓扑 |
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| 引用本文： | 罗淑珍,曾丽华,赖新兴. 循环群偏序集上的拓扑[J]. 江西师范大学学报(自然科学版), 2013, 0(1): 9-11 |
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| 作者姓名： | 罗淑珍 曾丽华 赖新兴 |
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| 作者单位： | 江西理工大学理学院,江西赣州,341000；江西理工大学南昌校区,江西南昌,330013 |
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| 基金项目： | 江西省教育厅2010年度青年科学基金(GJJ10155);江西理工大学校级科研基金(jxxj11068,jxxj12065)资助项目 |
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| 摘 要： | 利用循环群的特殊代数结构,引入了Scott子群拓扑σP(G),讨论了循环群偏序集上3种不同拓扑之间的关系,即循环群拓扑O(G)、Scott拓扑σ(G)和Scott子群拓扑σP(G),并得出若(G,O(G))是T0的紧空间且sub(G)分离G中的点,则CO(G)=σ(G)=σP(G).
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| 关 键 词： | 循环群偏序集 循环群拓扑 Scott拓扑 Scott子群拓扑 |
The Topologies on Cyclic Posets of Groups |
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| LUO Shu-zhen,ZENG Li-hua,LAI Xin-xing. The Topologies on Cyclic Posets of Groups[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2013, 0(1): 9-11 |
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| Authors: | LUO Shu-zhen ZENG Li-hua LAI Xin-xing |
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| Affiliation: | 1(1.Faculty of Science,Jiangxi University of Science and Technology,Ganzhou Jiangxi 341000,China; 2.Nanchang Campus,Jiangxi University of Science and Technology,Nanchang Jiangxi 330013,China) |
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| Abstract: | Based on the special structures of cyclic groups,the scott-subgroup topology σP(G) is introduced,and the relationshipes between the three differences topologies on cyclic groups are discussed,that is the cyclic topology O(G),the scott topology σ(G),the scott-subgroup topology σP(G).It is proved that if (G,O(G))is T0,compace space and sub(G)separate the points of groups G,then CO(G)=σ(G)=σP(G). |
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| Keywords: | cyclic posets of group cyclic topology Scott topology Scott-subgroup topology |
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