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Introduction. The class of finite dimensional projective geometries has been extended to include non-finite dimensional ones by J. von Neumann's remarkable discovery of continuous geometries.]; In an axiomatic formulation of the geometry as an irreducible complemented modular lattice § the finiteness of the dimensionality is guaranteed by a chain condition. Von Neumann drops this chain condition and, retaining explicitly only two of its weak consequences, namely, completeness of the geometrydoi:10.2307/1989895 fatcat:u456fyk53feqfpmxxhl5oar5za