$G$-Kernel-Open Sets, $G$-Kernel-Neighborhoods and $G$-Kernel-Derived Sets
Received:April 14, 2017  Revised:September 01, 2017
Key Word: topological spaces   $G$-methods   pointwise $G$-methods   $G$-hull-closed sets   $G$-kernel-open sets   $G$-kernel-neighborhoods   $G$-kernel-derived sets  
Fund ProjectL:Supported by the Special Youth Project of Ningde Normal University (Grant No.2016Q34) and the National Natural Science Foundation of China (Grant No.11471153).
Author NameAffiliation
Li LIU Institute of Mathematics, Ningde Normal University, Fujian 352100, P. R. China 
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      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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