Before revision: A pseudocircle is a simple closed curve on some surface . Arrangements of pseudocircles were introduced by Gr\"unbaum, who defined them as collections of pseudocircles that pairwise intersect in exactly two points, at which they cross.
After revision: A pseudocircle is a simple closed curve on some surface ; an arrangement of pseudocircles is a collection of pseudocircles that pairwise intersect in exactly two points, at which they cross.