Abstract
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generalization of matroids, oriented matroids, and linear subspaces of based vector spaces. This paper introduces the notion of a topological hyperfield and explores the generalization of Grassmannians and realization spaces to this context, particularly in relating the (hyper)fields R and C to hyperfields arising in matroid theory and in tropical geometry.
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