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Bibliography
Bennett, M. K. Affine Geometry: A Lattice Characterization. Proc. AMS 88 (1983), 21–26.
Bennett, M. K. Lattices of Convex Sets. Trans. AMS 234 (1977), 279–288.
Bennett, M. K. On Generating Affine Geometries. Alg. Univ. 4 (1974), 207–219.
Bennett, M. K. and G. Birkhoff. Convexity Lattices. To appear in Alg. Univ.
Bennett, M. K. and G. Birkhoff. A Peano Axiom for Convexity Lattices. To appear in Bull. Calcutta Math. Soc.
Birkhoff, G. "Lattice Theory", 3rd ed. Providence, AMS, 1967.
Gorn, S. On Incidence Geometries, Bull. AMS 46 (1940), 158–167.
Hilbert, D. "Foundations of Geometry", (transl. by E. J. Townsend), Open Court, La Salle, Ill. 1902.
Maeda, S. On Finite-Modular Atomistic Lattices. Alg. Univ. 12 (1981), 76–80.
Maeda, F. and S. Maeda. "Theory of Symmetric Lattices." Springer, New York, 1971.
Prenowitz, W., J. Jantosciak. "Join Geometries", Springer, Undergrad. Texts in Math. New York, 1979.
Rockafellar, T. "Convex Analysis," Princeton University Press, 1970.
Sasaki, U. Lattice Theoretic Characterization of Geometries Satisfying ‘Axiome der Verknüpfung.’ Hiroshima J. Ser. A, 16 (1953), 417–423.
Szmielew, W. The Role of the Pasch Axiom in the Foundations of Euclidean Geometry. In Proc. Tarski Symp., Proc. Symp. Pure Math. XXV, Providence, AMS 1974, 123–132.
Veblen, O. A New System of Axioms for Geometry. Trans. AMS 4 (1903), 343–384.
Wyler, O. Incidence Geometry. Duke Math. J. 20 (1953), 601–610.
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Bennett, M.K. (1985). Separation conditions on convexity lattices. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098453
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DOI: https://doi.org/10.1007/BFb0098453
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