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Morphisms of projective geometries and of corresponding lattices. (English) Zbl 0784.51003

The authors explore the well-known connection between projective geometries and projective lattices. The authors define the concept of morphism for projective geometries and for projective lattices. This enables the authors to extend the classical connection mentioned above to an equivalence between the category of projective geometries and the category of projective lattices. The article is well written and all results are clearly explained.

MSC:

51A05 General theory of linear incidence geometry and projective geometries
51D25 Lattices of subspaces and geometric closure systems
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References:

[1] Maeda, F. and Maeda, S.,Theory of Symmetric Lattices, Springer, Berlin, Heidelberg, New York, 1970. · Zbl 0219.06002
[2] Grätzer, G.,General Lattice Theory, Birkhäuser, Basel, Stuttgart, 1978. · Zbl 0385.06015
[3] Garner, L. E.,An Outline of Projective Geometry, North Holland, New York, Oxford, 1981. · Zbl 0462.51001
[4] Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D. S.,A Compendium of Continuous Lattices, Springer, Berlin, Heidelberg, New York, 1980. · Zbl 0452.06001
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