Further studies on open well-filtered spaces

TL;DR

This paper investigates properties of open well-filtered spaces, showing that their upper spaces also retain the open well-filtered property, and explores additional characteristics of these spaces.

Contribution

It extends the understanding of open well-filtered spaces by proving their stability under the upper space construction and analyzing further properties.

Findings

The upper space of an open well-filtered space is also open well-filtered.

Additional properties of open well-filtered spaces are identified and studied.

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.