Chong Shen ; Xiaoyong Xi ; Xiaoquan Xu ; Dongsheng Zhao - On open well-filtered spaces

lmcs:6041 - Logical Methods in Computer Science, December 18, 2020, Volume 16, Issue 4 -
On open well-filtered spacesArticle

Authors: Chong Shen ; Xiaoyong Xi ; Xiaoquan Xu ; Dongsheng Zhao

    We introduce and study a new class of $T_0$ spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered space; (2) every core-compact open well-filtered space is sober. As an immediate corollary, we deduce that every core-compact well-filtered space is sober. This provides another different and relatively more straight forward method to answer the open problem posed by Jia and Jung: Is every core-compact well-filtered space sober?

    Volume: Volume 16, Issue 4
    Published on: December 18, 2020
    Accepted on: October 20, 2020
    Submitted on: January 22, 2020
    Keywords: Mathematics - General Topology

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