Further studies on open well-filtered spaces
General Topology
2025-02-25 v2
Abstract
The open well-filtered spaces were introduced by Shen, Xi, Xu and Zhao to answer the problem whether every core-compact well-filtered space is sober. In the current paper we explore further properties of open well-filtered spaces. One of the main results is that if a space is open well-filtered, then so is its upper space (the set of all nonempty saturated compact subsets equipped with the upper Vietoris topology). Some other properties on open well-filtered spaces are also studied.
Cite
@article{arxiv.2211.16133,
title = {Further studies on open well-filtered spaces},
author = {Chong Shen and Xiaoyong Xi and Dongsheng Zhao},
journal= {arXiv preprint arXiv:2211.16133},
year = {2025}
}