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arXiv · 2001.07397

On open well-filtered spaces

Chong Shen·Xiaoyong Xi·Xiaoquan Xu·Dongsheng Zhao
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Abstract

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?

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Chong Shen, Xiaoyong Xi, Xiaoquan Xu, Dongsheng Zhao. 2020-12-17. On open well-filtered spaces. https://doi.org/10.23638/lmcs-16(4%3A18)2020

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