发表机构
School of Sciences, Southwest Petroleum University（西南石油大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究比Frechet-Urysohn空间更弱的序贯空间，证明了在特定条件下良滤空间的Scott拓扑与上Vietoris拓扑一致，以及ω-良滤coherent d-空间的sober性。
AI 中文摘要
近年来，在Domain理论的拓扑性质研究中，第一可数空间和Frechet-Urysohn空间受到密切关注并被频繁使用。本文聚焦于比Frechet-Urysohn空间更弱的序贯空间。主要结果如下：（1）对于良滤空间X，若PS(X)是序贯空间，则K(X)上的Scott拓扑与上Vietoris拓扑一致；（2）若X的乘积是序贯空间，则每个ω-良滤的coherent d-空间X是sober的。
英文摘要
Recently, in the study of topological properties in Domain theory, the first countable spaces and Frechet-Urysohn spaces receive close attention and are frequently employed. In this paper, we focus on sequential spaces weaker than Frechet-Urysohn spaces. The main results are: (1) For a well-filtered space X, the Scott topology and the upper vietoris topology on K(X) coincide if PS(X) is a sequential space; (2) every ω-well-filtered coherent d- space X is sober when the procuct of X is a sequential space.
