Corpus ID: 202712615

On $T_0$ spaces determined by well-filtered spaces

@article{Xu2019OnS,
  title={On \$T_0\$ spaces determined by well-filtered spaces},
  author={Xiao-quan Xu and Chong Shen and Xiaoyong Xi and Dongsheng Zhao},
  journal={arXiv: General Topology},
  year={2019}
}
  • Xiao-quan Xu, Chong Shen, +1 author Dongsheng Zhao
  • Published 2019
  • Mathematics
  • arXiv: General Topology
  • We first introduce and study two new classes of subsets in $T_0$ spaces - Rudin sets and $\wdd$ sets lying between the class of all closures of directed subsets and that of irreducible closed subsets. Using such subsets, we define three new types of topological spaces - $\mathsf{DC}$ spaces, Rudin spaces and $\wdd$ spaces. The class of Rudin spaces lie between the class of $\wdd$ spaces and that of $\dc$ spaces, while the class of $\dc$ spaces lies between the class of Rudin spaces and that of… CONTINUE READING

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