# 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} }

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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