A note on coherence of dcpos

Xiaodong Jia; Achim Jung; Qingguo Li

doi:10.1016/j.topol.2016.06.011

A note on coherence of dcpos

Xiaodong Jia
, Achim Jung
, Qingguo Li

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

252 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 language	English
Pages (from-to)	235-238
Number of pages	4
Journal	Topology and its Applications
Volume	209
Early online date	23 Jun 2016
DOIs	https://doi.org/10.1016/j.topol.2016.06.011
Publication status	Published - 15 Aug 2016

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10.1016/j.topol.2016.06.011

Jia_et_al_Note_on_coherence_dcpos_Topology_and_its_applications_AcceptedAccepted author manuscript, 71.1 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

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title = "A note on coherence of dcpos",

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.",

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AU - Jia, Xiaodong

AU - Jung, Achim

AU - Li, Qingguo

PY - 2016/8/15

Y1 - 2016/8/15

N2 - 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.

AB - 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.

U2 - 10.1016/j.topol.2016.06.011

DO - 10.1016/j.topol.2016.06.011

M3 - Article

SN - 0166-8641

VL - 209

SP - 235

EP - 238

JO - Topology and its Applications

JF - Topology and its Applications

ER -

A note on coherence of dcpos

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