Abstract:For A ⊆ ω, the coarse similarity class of A, denoted by [A], is the set of all B ⊆ ω such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric δ on the space S of coarse similarity classes defined by letting δ([A], [B]) be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We al… Show more
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