A note on coherence of dcpos

Xiaodong Jia, Achim Jung, Qingguo Li

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
117 Downloads (Pure)

Abstract

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 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 is compact in the Scott topology for every x,y∈L.
Original languageEnglish
Pages (from-to)235-238
Number of pages4
JournalTopology and its Applications
Volume209
Early online date23 Jun 2016
DOIs
Publication statusPublished - 15 Aug 2016

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