Ordered spaces and frames
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Priestley space

P000000

Compact Hausdorff space where for each pair of points x,y where x is not below y, there is a clopen upset U where x is in U and y is not in U.

Recorded examples

ValueIDNameReference
✓S000001The Rieger–Nishimura ladderEsakia, Heyting Algebras: Duality Theory (2019).
✓S000002Fine general frameBezhanishvili, Gabelaia and Jibladze (2022).
✓S000003Mardaev framesMardaev (1984); Almeida–Carai, Mardaev’s theorem via duality.
✓S000004WB graph frameBy definition
✓S000005Young lattice Fine frameConstruction definition
✓S000006Double omega frameConstruction definition
✓S000007Hyttinen–Martins–Moraschini–QuadrellaroHyttinen, Martins, Moraschini and Quadrellaro (2026), Definition 4.1.
✕S000008Bellissima’s constructionBellissima, Finitely generated free Heyting algebras (1986).
✓S000009Modified Rieger-Nishimura ladderEsakia, Heyting Algebras: Duality Theory (2019).
✓S000010Countable forkBy definition
✓S000011Countable co-forkBy definition
✓S000012Deleted top 2-chain spaceBy definition
✓S000013Deleted bottom 2-chain spaceBy definition