Remarks on affine complete distributive lattices

• Autorzy: Dominic Zypen
• Języki publikacji: EN

Abstrakty

EN

We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.

Słowa kluczowe

EN

Distributive lattice; affine complete; Priestley spaces; 06D50; 06D99

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 3
• Strony: 525-530

Daty

wydano

2006-09-01

online

2006-09-01

Twórcy

autor

Dominic Zypen

• Allianz Suisse

Bibliografia

• [1] B.A. Davey and H.A. Priestley: Lattices and Order, Cambridge University Press, 1990.
• [2] G. Grätzer: “Boolean functions on distributive lattices”, Acta Math. Acad. Sci. Hung., Vol. 15, (1964), pp. 195–201. http://dx.doi.org/10.1007/BF01897037
• [3] S. MacLane: Categories for the working mathematician, 2nd ed., Springer Verlag, (1998).
• [4] M. Ploščica: “Affine Complete Distributive Lattices”, Order, Vol. 11, (1994), pp. 385–390. http://dx.doi.org/10.1007/BF01108769
• [5] H.A. Priestley: “Representation of distributive lattices by means of ordered Stone spaces”, Bull. London Math. Soc., Vol. 2, (1970), pp. 186–190.
• [6] H.A. Priestley: “Ordered topological spaces and the representation of distributive lattices”, Proc. London Math. Soc., Vol. 3(24), (1972), pp. 507–530.
• [7] D. van der Zypen: Aspects of Priestley Duality, Thesis (PhD), University of Bern, 2004.

Identyfikatory

DOI

10.2478/s11533-006-0012-y