可数条件下Scott拓扑的sobriety性质
Sobriety of Scott topologies under countability conditions
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中文总结 AI 辅助
本文研究了可数条件下Scott拓扑的sobriety性质，证明了可数交连续核心紧dcpo和可数局部紧dcpo是sober的，但有理数空间的开集格不是sober的。
中文摘要 AI 辅助
本文关注可数情形下Scott拓扑的sobriety性质。具体地，我们证明：（1）每个满足交连续且核心紧的可数dcpo在Scott拓扑下是sober的；（2）每个可数局部紧dcpo赋予Scott拓扑后是sober的；（3）有理数空间Q的所有开集构成的格，在赋予Scott拓扑后不是sober的。
英文摘要
In this paper, we focus on the sobriety of the Scott topology in countable case. Specifically, we show that: (1) every meet-continuous core-compact countable dcpo is sober with respect to the Scott topology; (2)every countable locally compact dcpo is sober endowed with the Scott topology; (3) the lattice of all open sets for the rational numbers space Q equipped with the Scott topology is not sober.
发表机构
- School of Sciences, Southwest Petroleum University（西南石油大学理学院）
- School of Mathematics and Statistics, Shaanxi Normal University（陕西师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
