2025/03/17 by He, Zhengmao
#06B35 #06F30 #54B20 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2503.12766
In this paper, we investigate the sobriety of weakly first-countable spaces and give some sufficient conditions that the Scott topologies of the open set lattices are sober. The main results are: (1) Let P and Q be two posets. If ΣP× ΣQ is a Fréchet space, then Σ(P× Q)=ΣP × ΣQ. (2) For every ω-well-filtered coherent d-space X, if X× X is a Fréchet space, then X is sober; (3) For every ω type P-space or consonant Wilker space X, ΣO(X) is sober.