A note on coherence of dcpos

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• 作者：Xiaodong Jia^a ; ^{jia.xiaodong@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Achim Jung^a ; ^{A.Jung@cs.bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Qingguo Li^b ; ^{liqingguoli@aliyun.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54B20 ; 06B35 ; 06F30
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：209
• 期：Complete
• 页码：235-238
• 全文大小：222 K

文摘

In this note, we prove that a well-filtered dcpo L   is coherent in its Scott topology if and only if for every x,y∈L$x,y\in L$, ↑x∩↑y$\uparrow x\cap \uparrow y$ is compact in the Scott topology. We use this result to prove that a well-filtered dcpo L is Lawson-compact if and only if it is patch-compact if and only if L   is finitely generated and ↑x∩↑y$\uparrow x\cap \uparrow y$ is compact in the Scott topology for every x,y∈L$x,y\in L$.