Von Neumann worked on lattice theory between 1937 and 1939. Von Neumann provided an abstract exploration of dimension in completed complemented modular topological lattices: "Dimension is determined, up to a positive linear transformation, by the following two properties. It is conserved by perspective mappings ("perspectivities") and ordered by inclusion. The deepest part of the proof concerns the equivalence of perspectivity with "projectivity by decomposition"—of which a corollary is the transitivity of perspectivity." Garrett Birkhoff writes: "John von Neumann's brilliant mind blazed over lattice theory like a meteor". COUNT 3
QSN1 What did von Neumann work on in 1937 - 39? ANS1 lattice theory QSN2 What properties determine dimension in lattice theory? ANS2 conserved by perspective mappings ("perspectivities") and ordered by inclusion QSN3 Who wrote that "John von Neumann's brilliant mind blazed over lattice theory like a meteor?" ANS3 Garrett Birkhoff