Abstract
Here we look back at some work done in the mid-1980s in collaboration with Laszlo Lovasz. Our main concern at that time was to provide conditions that make it possible to pass to the limit of a class of finite matroids. With the current flurry of interest in limits of combinatorial objects, a review of such matroid limits seems timely. The characteristic property of a continuous matroid is the existence of a rank function taking as values the full real unit interval. Known examples of such rank functions include Lebesgue measure on the unit interval and the dimension function of certain von Neumann algebras. In both these cases the lattice property of modularity plays a crucial role. A more general concept, pseudomodularity, makes possible the construction of e.g. continuous field extensions (algebraic matroids) and continuous partition lattices (graphic matroids).
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