刘丽.$G$核开集,$G$核邻域与$G$ 核导集[J].数学研究及应用,2018,38(3):276~286
$G$核开集,$G$核邻域与$G$ 核导集
$G$-Kernel-Open Sets, $G$-Kernel-Neighborhoods and $G$-Kernel-Derived Sets
投稿时间:2017-04-14  修订日期:2017-09-01
DOI:10.3770/j.issn:2095-2651.2018.03.006
中文关键词:  拓扑空间  $G$方法  点式$G$方法  $G$壳闭集  $G$核开集  $G$核邻域  $G$核导集
英文关键词:topological spaces  $G$-methods  pointwise $G$-methods  $G$-hull-closed sets  $G$-kernel-open sets  $G$-kernel-neighborhoods  $G$-kernel-derived sets
基金项目:宁德师范学院青年专项类项目(Grant No.2016Q34);国家自然科学基金资助项目(Grant No.11471153).
作者单位
刘丽 宁德师范学院, 福建 宁德 352100 
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中文摘要:
      在拓扑空间中, 在$G$方法意义下以$G$壳与$G$核为基础, 引入$G$壳闭集,$G$核开集,$G$核邻域与$G$核导集的概念, 讨论其相应的一些性质. 特别的, 定义了点式$G$方法, 提供了在此方法下$G$闭集与$G$壳闭集, $G$开集与$G$核开集, $G$邻域与$G$核邻域, $G$导集与$G$核导集的一致性, 丰富了拓扑空间中关于$G$闭集, $G$开集, $G$内部, $G$邻域和$G$导集的一些结果. 同时, 提出一些问题以供进一步研究.
英文摘要:
      Based on $G$-hulls and $G$-kernels under the meaning of $G$-methods on sets, we introduce the concepts of $G$-hull-closed sets, $G$-kernel-open sets, $G$-kernel-neighborhoods and ~$G$-kernel-derived sets, discuss some related properties. In particular, we define pointwise $G$-methods, prove the consistency of $G$-closed sets and $G$-hull-closed sets, $G$-open sets and $G$-kernel-open sets, $G$-neighborhoods and $G$-kernel-neighborhoods, $G$-derived sets and~$G$-kernel-derived sets under this method, and enrich some results about $G$-closed sets, $G$-open sets, $G$-interiors, $G$-neighborhoods and $G$-derived sets in sets. At the same time, we put forward some problems for further research.
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