| $G$-Kernel-Open Sets, $G$-Kernel-Neighborhoods and $G$-Kernel-Derived Sets |
| Received:April 14, 2017 Revised:September 01, 2017 |
| Key Words:
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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| Fund Project:Supported by the Special Youth Project of Ningde Normal University (Grant No.2016Q34) and the National Natural Science Foundation of China (Grant No.11471153). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.03.006 |
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