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 language | English |
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Pages (from-to) | 235-238 |
Number of pages | 4 |
Journal | Topology and its Applications |
Volume | 209 |
Early online date | 23 Jun 2016 |
DOIs | |
Publication status | Published - 15 Aug 2016 |