广义拓扑空间中滤子的一些结果  

Some Results of Filters in Generalized Topological Spaces

作　　者：郭俊 朱培勇[1] GUO Jun;ZHU Peiyong(School of Mathmatical Science, University of Electronic Science and Technology of China, Chengdu 611731, China)

机构地区：[1]电子科技大学数学科学学院

出　　处：《四川理工学院学报（自然科学版）》2019年第3期95-100,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学青年基金(11501391)

摘　　要：类比一般拓扑在广义拓扑空间中引入滤子的概念,并且在此空间中讨论了滤子的广义聚点、广义极限点及其映射连续性。获得了如下结论:关于广义拓扑空间中广义聚点的三条等价性结果;在特定条件下,广义聚点集与广义极限点集的一致性;广义Hausdorff空间中滤子极限点的唯一性;并且在广义拓扑空间中给出并证明了滤子映射连续的五个等价刻画和开映射的五个等价刻画。在此基础上给出了滤子在网领域上的一些应用。最后指出:广义拓扑空间的这些性质在下半拓扑空间中也成立。研究结果使一般拓扑空间中滤子的相关理论得到推广与扩充。The concept of filter of generalized topological spaces is introduced by the comparison of topological spaces.And in this space,the generalized accumulation point of the filter,the generalized limit point and its mapping continuity are discussed. The following conclusions are obtained: the three equivalence results for generalized aggregation points in generalized topological spaces;Under certain conditions,the consistency of generalized accumulation set and generalized limit set is obtained. Uniqueness of generalized limit points of filters in generalized Hausdorff spaces. In the generalized topological spaces,five continuous equivalent characterizations of the filter mapping and five equivalent characterizations of the open mapping are given and proved. On this basis,some applications of filters in the field of network are given. Finally,the properties of the generalized topological spaces also hold in the inf-semi-topological spaces. The results have promoted and expanded the relevant theory of filters in general topological spaces.

关 键 词：广义拓扑空间 下半拓扑空间 滤子 广义极限 广义聚点 映射 

分 类 号：O189.11[理学—数学]