# Remarks on affine complete distributive lattices

Open Mathematics (2006)

- Volume: 4, Issue: 3, page 525-530
- ISSN: 2391-5455

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topDominic Zypen. "Remarks on affine complete distributive lattices." Open Mathematics 4.3 (2006): 525-530. <http://eudml.org/doc/269587>.

@article{DominicZypen2006,

abstract = {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.},

author = {Dominic Zypen},

journal = {Open Mathematics},

keywords = {06D50; 06D99},

language = {eng},

number = {3},

pages = {525-530},

title = {Remarks on affine complete distributive lattices},

url = {http://eudml.org/doc/269587},

volume = {4},

year = {2006},

}

TY - JOUR

AU - Dominic Zypen

TI - Remarks on affine complete distributive lattices

JO - Open Mathematics

PY - 2006

VL - 4

IS - 3

SP - 525

EP - 530

AB - 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.

LA - eng

KW - 06D50; 06D99

UR - http://eudml.org/doc/269587

ER -

## References

top- [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 Zbl0146.01902
- [3] S. MacLane: Categories for the working mathematician, 2nd ed., Springer Verlag, (1998). Zbl0705.18001
- [4] M. Ploščica: “Affine Complete Distributive Lattices”, Order, Vol. 11, (1994), pp. 385–390. http://dx.doi.org/10.1007/BF01108769 Zbl0816.06010
- [5] H.A. Priestley: “Representation of distributive lattices by means of ordered Stone spaces”, Bull. London Math. Soc., Vol. 2, (1970), pp. 186–190. Zbl0201.01802
- [6] H.A. Priestley: “Ordered topological spaces and the representation of distributive lattices”, Proc. London Math. Soc., Vol. 3(24), (1972), pp. 507–530. Zbl0323.06011
- [7] D. van der Zypen: Aspects of Priestley Duality, Thesis (PhD), University of Bern, 2004.

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