Abstract
A lattice is defined as a partially ordered set in which any two elements have a least upper bound and a greatest lower bound. In any complete lattice there exist a zero element “0” and a unit element “1” such that 0 ≤ x ≤ 1 for every lattice element x. The chapter considers lattices that are not distributive. The applications of lattice theory to the axiomatization of geometry yields radically different and simple characterizations of the geometries considered. Modular lattices can be regarded as a generalization of projective geometry. It is more reasonable to consider only complemented modular lattices because every projective lattice is complemented.. In context to lattice-theoretic approach, the chapter discusses results of projective and affine geometry and their generalizations.
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