Corpus ID: 208512833

First countability, $\omega$-well-filtered spaces and reflections

  title={First countability, \$\omega\$-well-filtered spaces and reflections},
  author={X. Xu and C. Shen and Xiaoyong Xi and Dongsheng Zhaod},
  journal={arXiv: General Topology},
  • X. Xu, C. Shen, +1 author Dongsheng Zhaod
  • Published 2019
  • Mathematics
  • arXiv: General Topology
  • We first introduce and study two new classes of subsets in $T_0$ spaces - $\omega$-Rudin sets and $\omega$-well-filtered determined sets lying between the class of all closures of countable directed subsets and that of irreducible closed subsets, and two new types of spaces - $\omega$-$d$ spaces and $\omega$-well-filtered spaces. We prove that an $\omega$-well-filtered $T_0$ space is locally compact iff it is core compact. One immediate corollary is that every core compact well-filtered space… CONTINUE READING
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