<p>In this paper, we present a Priestley-type topological representation for <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12_2025_907_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\prec $</EquationSource> <EquationSource Format="MATHML"><math> <mo>≺</mo> </math></EquationSource> </InlineEquation>-distributive <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12_2025_907_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\vee $</EquationSource> <EquationSource Format="MATHML"><math> <mo>∨</mo> </math></EquationSource> </InlineEquation>-predomains, thereby answering an open problem posed by T. Bice. Moreover, we establish a dual equivalence between the category of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12_2025_907_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\prec $</EquationSource> <EquationSource Format="MATHML"><math> <mo>≺</mo> </math></EquationSource> </InlineEquation>-distributive <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12_2025_907_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\vee $</EquationSource> <EquationSource Format="MATHML"><math> <mo>∨</mo> </math></EquationSource> </InlineEquation>-predomains with <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12_2025_907_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\prec $</EquationSource> <EquationSource Format="MATHML"><math> <mo>≺</mo> </math></EquationSource> </InlineEquation>-morphisms and that of DP-compact pospaces with DP-morphisms. In particular, our results restrict to Hansoul-Poussart duality for bounded distributive sup-semilattices and to a Priestley duality for continuous frames.</p>

The Priestley duality for $\prec $-distributive $\vee $-predomains

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发表日期：

2025年9月29日

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Ao Shen,
Xiaodong Jia,
Hualin Miao,
Qingguo Li

摘要

In this paper, we present a Priestley-type topological representation for $\prec $ $≺$ -distributive $\vee $ $\lor$ -predomains, thereby answering an open problem posed by T. Bice. Moreover, we establish a dual equivalence between the category of $\prec $ $≺$ -distributive $\vee $ $\lor$ -predomains with $\prec $ $≺$ -morphisms and that of DP-compact pospaces with DP-morphisms. In particular, our results restrict to Hansoul-Poussart duality for bounded distributive sup-semilattices and to a Priestley duality for continuous frames.

The Priestley duality for \(\prec \)-distributive \(\vee \)-predomains

摘要