On open well-filtered spaces
General Topology
2023-06-22 v4
Abstract
We introduce and study a new class of 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?
Cite
@article{arxiv.2001.07397,
title = {On open well-filtered spaces},
author = {Chong Shen and Xiaoyong Xi and Xiaoquan Xu and Dongsheng Zhao},
journal= {arXiv preprint arXiv:2001.07397},
year = {2023}
}