A note on coherence of dcpos
| Autor: | Qingguo Li, Xiaodong Jia, Achim Jung |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Complete partial order 010102 general mathematics 0102 computer and information sciences Coherence (statistics) 01 natural sciences Combinatorics Mathematics::Logic 010201 computation theory & mathematics If and only if Computer Science::Logic in Computer Science Geometry and Topology Finitely-generated abelian group 0101 mathematics Topology (chemistry) Mathematics |
| Zdroj: | Topology and its Applications. 209:235-238 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2016.06.011 |
| Popis: | 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 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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