~$G$-KERNEL-OPEN SETS,~$G$-KERNEL-NEIGHBORHOODS AND ~$G$-KERNEL-DERIVED SETS
~$G$-KERNEL-OPEN SETS,~$G$-KERNEL-NEIGHBORHOODS AND ~$G$-KERNEL-DERIVED SETS
投稿时间:2017-04-14  最后修改时间:2017-08-05
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中文关键词:  
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.
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作者单位E-mail
liuli 宁德师范学院 429378220@qq.com 
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中文摘要:
      
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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