  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.
