A discussion of well-filteredness and sobriety
The authors work in the framework of directed complete partially ordered sets, and items related to the notion of soberness. In this paper, they give a sufficient condition for a core-compact dcpo to be sober. Then they introduce and study a new kind of posets, namely the so-called join continuous posets. Also, they settle and analyze several relationships arising among sober, well-filtered and weak well-filtered topological properties. Based on the results they get, some characterizations for a poset to be Lawson compact are achieved. Moreover, they solve some open questions issued in this literature, posed by \textit{X. Xu} and \textit{D. Zhao} [Topology Appl. 272, Article ID 107080, 14 p. (2020; Zbl 1477.06020)].
scientific article; zbMATH DE number 7318660
scientific article