Some open problems on well-filtered spaces and sober spaces

TL;DR

This paper surveys recent progress in the study of sober and well-filtered spaces, highlighting key developments and presenting open problems to guide future research in domain theory and topology.

Contribution

It provides a concise overview of recent advances and introduces open problems in the area of sober and well-filtered spaces.

Findings

Summarizes recent breakthroughs in sober and well-filtered spaces

Poses open problems to stimulate further research

Highlights key developments in domain theory and topology

Abstract

In the past few years, the research on sober spaces and well-filtered spaces has got some breakthrough progress. In this paper, we shall present a brief summarising survey on some of such development. Furthermore, we shall pose and illustrate some open problems on well-filtered spaces and sober spaces.