循环群偏序集上的拓扑
The Topologies on Cyclic Posets of Groups

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).
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)